×

Partial stability and control: the state-of-the-art and future trends. (English. Russian original) Zbl 1095.93023

Autom. Remote Control 66, No. 4, 511-561 (2005); translation from Avtom. Telemekh. 2005, No. 4, 3-59 (2005).
Summary: Problems in bordering fields associated with partial stability and stabilization of nonlinear dynamic systems, including partial stability and stabilization by part of coordinates of the phase vector, are reviewed. They are classified, and their relation with other stability and stabilization problems, including recent ones, are considered. Main development trends in theory and research methods are surveyed and certain results and applications are described. The partial control notion in border disciplines is examined. A long list of references is given.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
34D05 Asymptotic properties of solutions to ordinary differential equations
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akulenko, L.D., Asymptoticheskie metody optimal?nogo upravleniya (Asymptotic Optimal Control Methods), Moscow: Nauka, 1987. · Zbl 0626.49002
[2] Aleksandrov, A.Yu., Asymptotic Stability of the Solution of Nonlinear Nonautonomous Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1999, no. 2, pp. 5-9. · Zbl 1077.34513
[3] Aleksandrov, A.Yu., Stability of a Class of Nonlinear Systems, Prikl. Mat. Mekh., 2000, vol. 64, no.4, pp. 545-550. · Zbl 0988.70017
[4] Alekseeva, S.A., Vorotnikov, V.I., and Feofanova, V.A., Partial Equiasymptotic Stability of Nonlinear Dynamic Systems, Avtom. Telemekh., 2005, no. 2, pp. 3-16.
[5] Aminov, A.B. and Sirazetdinov, T.K., The Lyapunov Functions Method in Problems of Semistability of Motion, Prikl. Mat. Mekh., 1987, vol. 51, no.5, pp. 709-716. · Zbl 0677.70023
[6] Anapol?skii, L.Yu. and Chaikin, S.V., Stability in Part of Variables of Relative Equilibrium of an Elastic Satellite, Prikl. Mat. Mekh., 1993, vol. 57, no.2, pp. 67-76.
[7] Anashkin, O.V. and Khapaev, M.M., Partial Stability of Nonlinear Systems of Ordinary Differential Equations with a Small Parameter, Diff. Uravn., 1995, vol. 31, no.3, pp. 371-381. · Zbl 0853.34043
[8] Andreev, A.S., Asymptotic Stability and Instability of Nonautonomous Systems, Prikl. Mat. Mekh., 1979, vol. 43, no.5, pp. 796-805. · Zbl 0452.34044
[9] Andreev, A.S., Asymptotic Stability and Instability of the Zero Solution of a Nonautonomous System to Part of Variables, Prikl. Mat. Mekh., 1984, vol. 48, no.5, pp. 707-713.
[10] Andreev, A.S., Study of Partial Asymptotic Stability and Instability via Limiting Equations, Prikl. Mat. Mekh., 1987, vol. 51, no.2, pp. 253-259.
[11] Andreev, A.S., Studies of Partial Asymptotic Stability, Prikl. Mat. Mekh., 1991, vol. 55, no.4, pp. 539-547.
[12] Andreev, A.S., Stability of Equilibrium Positions of a Nonautonomous Mechanical System, Prikl. Mat. Mekh., 1996, vol. 60, no.3, pp. 388-396. · Zbl 0925.70229
[13] Andreev, A.S. and Pavlikov, S.V., Partial Stability of Nonautonomous Functional Differential Equations, Prikl. Mat. Mekh., 1999, vol. 63, no.1, pp. 3-12. · Zbl 0942.34064
[14] Andrievskii, B.R. and Fradkov, A.L., Izbrannye glavy teorii avtomaticheskogo upravleniya s primerami na yazyke MATLAB (Selected Topics in Automatic Control Theory and Examples in MATLAB), St. Petersburg: Nauka, 1999. · Zbl 0964.93005
[15] Andrievskii, B.R. and Fradkov, A.L., Control of Chaos: Methods and Applications. I. Methods, Avtom. Telemekh., 2003, no. 5, pp. 3-45. · Zbl 1107.37302
[16] Bakan, G.M., Volosov, V.V., and Kussul?, N.N., State Estimation for Continuous Dynamic Systems by the Ellipsoid Method, Kibern. Sist. Analiz, 1996, vol. 32, no.6, pp. 72-91. · Zbl 0906.93034
[17] Burkov, I.V., Stabilization of Natural Mechanical Systems without Velocity Measurements and Application to Control a Solid, Prikl. Mat. Mekh., 1998, vol. 62, no.6, pp. 923-933.
[18] Vavilov, P.A. and Prokop?ev, V.P., Partial Stability of Motion of Linear Difference Systems, in Ustoichivost? i nelineinye kolebaniya (Stability and Nonlinear Oscillations), Sverdlovsk: Ural. Gos. Univ., 1986, pp. 3-6.
[19] Vorotnikov, V.I., Partial Stability of Motion of Certain Nonlinear Systems, Prikl. Mat. Mekh., 1979, vol. 43, no.3, pp. 441-450. · Zbl 0444.70024
[20] Vorotnikov, V.I., Partial Stability of Motion, Prikl. Mat. Mekh., 1988, vol. 52, no.3, pp. 372-385. · Zbl 0708.34049
[21] Vorotnikov, V.I., Ustoichivost? dinamicheskikh sistem po otnosheniyu k chasti peremennykh (Stability of Dynamic Systems to Part of Variables), Moscow: Nauka, 1991. · Zbl 0734.93063
[22] Vorotnikov, V.I., Problems and Investigation Methods of Partial Stability and Stabilization of Motion: Trends, Results, and Specifics, Avtom. Telemekh., 1993, no. 3, pp. 3-62.
[23] Vorotnikov, V.I., Partial Stability Theory, Prikl. Mat. Mekh., 1995, vol. 59, no.4, pp. 553-561. · Zbl 0900.70291
[24] Vorotnikov, V.I., Barbashin-Krasovskii Theorems in Partial Stability Problems, Dokl. Ross. Akad. Nauk, 1997, vol. 354, no.4, pp. 481-484. · Zbl 1050.34514
[25] Vorotnikov, V.I., Partial Zero-Controllability of Nonlinear Dynamic Systems, Avtom. Telemekh., 1997, no. 6, pp. 50-63. · Zbl 0935.93016
[26] Vorotnikov, V.I., Partial Stability Problems, Prikl. Mat. Mekh., 1999, vol. 63, no.5, pp. 736-745.
[27] Vorotnikov, V.I., A Nonlinear Game Problem on Reorientation of an Asymmetric Solid Body, Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, 1999, no. 1, pp. 3-18.
[28] Vorotnikov, V.I., Two Classes of Partial Stability Problems: Unification of Concepts and Unified Solvability Conditions, Dokl. Ross. Akad. Nauk, 2002, vol. 384, no.1, pp. 47-51.
[29] Vorotnikov, V.I., Stability and Partial Stability of Equilibrium Positions of Nonlinear Dynamic Systems, Dokl. Ross. Akad. Nauk, 2003, vol. 389, no.3, pp. 332-337.
[30] Vorotnikov, V.I., Coordinate Synchronization of Dynamic Systems, Diff. Uravn., 2004, vol. 40, no.1, pp. 5-23.
[31] Vorotnikov, V.I., Partial Global Asymptotic Stability, Dokl. Ross. Akad. Nauk, 2004, vol. 396, no.3, pp. 295-299. · Zbl 1282.34057
[32] Vorotnikov, V.I. and Prokop?ev, V.P., Partial Stability of Motion of Linear Systems, Prikl. Mat. Mekh., 1978, vol. 42, no.2, pp. 268-271.
[33] Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost? i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya metody i prilozhemiya (Stability and Control of Dynamic systems by Part of Phase Vector Coordinates: Theory, Methods, and Applications), Moscow: Nauchnyi Mir, 2001. · Zbl 1016.34052
[34] Vyiichich, V.A. and Kozlov, V.V., Lyapunov-Stability to Given State Functions, Prikl. Mat. Mekh., 1991, vol. 55, no.4, pp. 555-559.
[35] Galiullin, A.S., Mukhametzyanov, I.A., Mukharlyamov, R.G., and Furasov, V.D., Postroenie sistem programmnogo dvizheniya (Design of Systems of Programmed Motion), Moscow: Nauka, 1971. · Zbl 0233.70002
[36] Gal?perin, E.A. and Yaroslavtsev, A.A., Partial Stabilization of Steady Motion of Nonlinear Control Systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1969, no. 5, pp. 140-147.
[37] Demin, V.G., The Rumyantsev Partial Stability Theorem: Its Application in Celestial Mechanics, Kosm. Issl., 1964, vol. 2, no.5, pp. 416-418.
[38] Demin, V.G., Dvizhenie iskusstvennogo sputnika v netsentral?nom pole tyagoteniya (Motion of an Artificial Satellite in a Noncentral Attraction Field), Moscow: Nauka, 1968.
[39] Demin, V.G. and Furasov, V.D., Partial Stabilization of Control Systems, Prikl. Mat. Mekh., 1976, vol. 40, no.2, pp. 355-359. · Zbl 0355.93023
[40] Druzhinina, O.V. and Shestakov, A.A., The Generalized Lyapunov Direct Method for Problems of Stability and Attraction of Time Systems, Mat. Sb., 2002, vol. 193, no.10, pp. 17-48. · Zbl 1129.93469
[41] Zaitsev, V.V., Criteria for the Existence and Estimation of Invariant Constraints on Sets of Autonomous Systems of Differential Equations, Diff. Uravn., 1993, vol. 20, no.5, pp. 766-772. · Zbl 0835.34048
[42] Zubov, V.I., Matematicheskie metody issledovaniya sistem avtomaticheskogo regulirovaniya (Mathematical Research Methods for Automatic Control Systems), Leningrad: Sudpromgiz, 1959. · Zbl 0088.10102
[43] Zubov, V.I., Dinamika upravlyaemykh protsessov (Dynamics of Controlled Processes), Moscow: Vysshaya Shkola, 1982. · Zbl 0535.93001
[44] Zuev, A.L., Partial Stabilization of Nonautonomous Systems by Lyapunov Control Functions, Probl. Upravlen. Informatiki, 2000, vol. 32, no.4, pp. 25-34.
[45] Ignat?ev, A.O., Partial Stability of Motion under Constant Perturbations, Mat. Fiz. Nelineinaya Mekh., 1988, no. 10, pp. 20-25.
[46] Ignat?ev, A.O., Conservation of Uniform Partial Asymptotic Stability, Prikl. Mat. Mekh., 1989, vol. 53, no.1, pp. 167-171.
[47] Ignat?ev, A.O., Partial Stability of Almost-Periodic Systems, Diff. Uravn., 1989, vol. 25, no.8, pp. 1446-1448. · Zbl 0682.34040
[48] Ignat?ev, A.O., Partial Equiasymptotic Stability, Prikl. Mat. Mekh., 1999, vol. 63, no.5, pp. 871-875.
[49] Ignat?ev, A.O., Partial Stability in Functional Differential Delay Systems, Mekh. Tverdogo Tela, 2000, no. 30, pp. 158-164.
[50] Il?yasov, K., Partial Stability of Hereditary Systems, Mat. Fiz., 1982, no. 31, pp. 32-36.
[51] Il?yasov, K., Partial Stability of the Solutions of Linear Difference Equations, Mat. Fiz., 1984, no. 35, pp. 30-32.
[52] Kadiev, R.I., Sufficient Conditions for the Partial Stability of Linear Stochastic Hereditary Systems, Izv. Vuzov. Mat., 2000, vol. 44, no.6, pp. 75-79. · Zbl 0999.60055
[53] Kadiev, R.I., Partial Stability of the Solutions of Stochastic Functional Differential Equations in First Approximation, Izv. Vuzov. Mat., 2001, vol. 45, no.5, pp. 30-35. · Zbl 0996.60063
[54] Kalistratova, M.A., Partial Stability of Delay Systems, Avtom. Telemekh., 1986, no. 5, pp. 32-37. · Zbl 0612.93053
[55] Karapetyan, A.V., Permanent Rotations of a Heavy Solid on an Absolutely Rough Horizontal Plane, Prikl. Mat. Mekh., 1981, vol. 45, no.5, pp. 808-814. · Zbl 0493.73015
[56] Karapetyan, A.V., Ustoichivost? statsionarnykh dvizhenii (Stability of Stationary Motion), Moscow: Editorial, 1998.
[57] Karapetyan, A.V. and Rumyantsev, V.V., Stability of Conservative and Dissipative Systems, Itogi Nauki Tekh., Obshch. Mekh., 1983, vol. 6, pp. 3-127. · Zbl 0596.70024
[58] Karimov, A.U., Partial Stability under Constant Perturbations, in Mat. Fiz. Elektrodinamika, Moscow: Mosk. Gos. Univ., 1973, pp. 3-10.
[59] Karnishin, S.G., Partial Stability of Functional Differential Equations, in Funktsional?no differentsial?nye uravneniya (Functional Differential Equations), Perm: Perm. Pedag. Inst., 1987.
[60] Kovalev, A.M., Partial Controllability of Dynamic Systems, Prikl. Mat. Mekh., 1993, vol. 57, no.6, pp. 41-50.
[61] Kovalev, A.M., Partial Stability and Stabilization of Dynamic systems, Ukr. Math. Zh., 1995, vol. 47, no.2, pp. 186-193. · Zbl 0938.34058
[62] Kozlov, V.V., Stability of Equilibrium Positions in a Nonstationary Force Field, Prikl. Mat. Mekh., 1991, vol. 51, no.1, pp. 12-19.
[63] Kolmanovskii, V.B. and Nosov, V.R., Ustoichivost? i periodicheskie rezhimy reguliruemykh sistem s posledeistviem (Stability and Periodic States of Hereditary Control Systems), Moscow: Nauka, 1981.
[64] Kosov, A.A., K zadache ob ustoichivosti dvizheniya otnositel?no chasti peremennykh: voprosy kachestv. teorii diff. uravnenii (Partial Stability of Motion: A Qualitative Theory of Differential Equations), Novosibirsk: Nauka, 1988.
[65] Krasovskii, N.N., Teoriya upravleniya dvizheniem (Motion Control Theory), Moscow: Nauka, 1968.
[66] Krasovskii, N.N., Igrovye zadachi o vstreche dvizhenii (Game Problems of Counter Motions), Moscow: Nauka, 1970.
[67] Krementulo, V.V., Stabilizatsiya statsionarnykh dvizhenii tverdogo tela pri pomoshchi vrashchayushchikhsya mass (Stabilization of Stationary Motion of a Solid by a Rotating Mass), Moscow: Nauka, 1977.
[68] Krivosheev, Yu.A. and Lutsenko, A.V., Partial Stability of Motion of Linear Systems with Constant and Almost Constant Matrices, Prikl. Mat. Mekh., 1980, vol. 44, no.2, pp. 205-210.
[69] Kurakin, L.G., Stability of a Proper Vortex n-gon, Dokl. Ross. Akad. Nauk, 1994, vol. 335, no.6, pp. 729-731.
[70] Lizunova, M.G., Ob ustoichivosti otnositel?no chasti peremennykh v kriticheskom sluchae pary chisto mnimykh kornei: ustoichivost? i nelineinye kolebaniya (Partial Stability under a Critical Pair of Purely Imaginary Roots: Stability and Nonlinear Oscillations), Sverdlovsk: Ural. Gos. Univ., 1991.
[71] Lilov, L.K., Partial Stabilization of Stationary Motion of Mechanical Systems, Prikl. Mat. Mekh., 1972, vol. 36, no.6, pp. 977-985.
[72] Lutsenko, A.V. and Stadnikova, L.V., Partial Stability in First Approximation, Diff. Uravn., 1973, vol. 9, no.8, pp. 1530-1533.
[73] Lyapunov, A.M., Issledovanie odnogo iz osobennykh sluchaev zadachi ob ustoichivosti dvizheniya (A Special Case of Stability of Motion), Sobr. Soch. (Collected Works), Moscow: Akad. Nauk SSSR, 1956, vol. 2.
[74] Lyao Syao Sin, Partial Asymptotic Stability of Motion of Linear Systems, Prikl. Mat. Mekh., 1989, vol. 53, no.6, pp. 1034-1035.
[75] Malkin, I.G., Stability of Motion in Lyapunov?s Sense, Mat. Sb., 1938, vol. 3(45), no. 1, pp. 47-100.
[76] Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Stability of Motion), Moscow: Nauka, 1966.
[77] Mamedova, T.F., Asymptotic Equivalence of Differential Equations and Partial Stability of Solutions, Proc. Int. Mat. Conf. ?Differential Equations and Their Applications,? Saransk: Saransk. Gos. Univ., 1995. · Zbl 0974.34518
[78] Martynyuk, A.A., Technical Stability of Motion to a Set of Given Coordinates, Prikl. Mat. Mekh., 1972, vol. 8, no.3, pp. 87-91.
[79] Martynyuk, A.A., Prakticheskaya ustoichivost? dvizheniya (Practical Stability of Motion), Kiev: Naukova Dumka, 1983. · Zbl 0539.70031
[80] Martynyuk, A.A., Partial Semistability of Motion, Dokl. Ross. Akad. Nauk, 1992, vol. 324, no.1, pp. 39-41.
[81] Martynyuk, A.A., Semistability?A New Trend in Analysis of Nonlinear Systems, Prikl. Mekh., 1994, vol. 30, no.5, pp. 3-17.
[82] Martynyuk, A.A. and Chernetskaya, L.N., Semistability of Linear Autonomous Systems, Dokl. Akad. Nauk Ukrainy, 1993, no. 8, pp. 17-19. · Zbl 0891.34056
[83] Martynyuk, A.A. and Chernetskaya, L.N., Semistability of Linear Periodic-Coefficient Systems, Dokl. Akad. Nauk Ukrainy, 1993, no. 11, pp. 61-65. · Zbl 0891.34056
[84] Matrosov, V.M., Theory of Stability of Motion, Prikl. Mat. Mekh., 1962, vol. 26, no.6, pp. 992-1002. · Zbl 0125.05003
[85] Matrosov, V.M., Development of the Lyapunov Functions Method in Stability Theory, Tr. II Vses. S? ezda po Teor. i Prikl. Mekh. (Proc. II All-Union Congress: Theoretical and Applied Mechanics), Moscow: Nauka, 1965, vol. 1, pp. 112-125.
[86] Matrosov, V.M., Principles of Comparison with Lyapunov?s Vector Functions. Part 4, Diff. Uravn., 1969, vol. 5, no.12, pp. 2129-2143.
[87] Miroshnik, I.V., Partial Stability and Geometric Problems of Nonlinear Dynamics, Avtom. Telemekh., 2002, no. 11, pp. 39-55. · Zbl 1107.34334
[88] Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complicated Dynamic Systems), St. Petersburg: Nauka, 2000. · Zbl 0962.93001
[89] Mitropol?skii, Yu.A. and Lykova, O.B., Integral?nye mnogoobraziya v nelineinoi mekhanike (Integral Manifolds in Nonlinear Mechanics), Moscow: Nauka, 1973.
[90] Movchan, A.A., Stability of Processes in Two Metrics, Prikl. Mat. Mekh., 1960, vol. 24, no.6, pp. 988-1001.
[91] Moiseev, N.N. and Rumyantsev, V.V., Dinamika tela s polostyami, soderzhashchimi zhidkost? (Dynamics of Bodies with Liquid-filled Hollows), Moscow: Nauka, 1965.
[92] Mukharlyamov, R.G., Control of Programmed Partial Motion, Diff. Uravn., 1989, vol. 25, no.8, pp. 938-942. · Zbl 0703.49004
[93] Nabiullin, M.K., Statsionarnye dvizheniya i ustoichivost? uprugikh sputnikov (Stationary Motion and Stability of Elastic Satellites), Novosibirsk: Nauka, 1990. · Zbl 0717.70022
[94] Nosov, V.R. and Furasov, V.D., Stability of Discrete-Time Processes to Given Variables and Convergence of Certain Optimization Algorithms, Zh. Vychisl. Mat. Mat.Fiz., 1979, vol. 19, no.2, pp. 316-328.
[95] Oziraner, A.S., Partial Stability of Motion, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1971, no. 1, pp. 92-100. · Zbl 0234.34064
[96] Oziraner, A.S., Certain Theorems of the Second Lyapunov Method, Prikl. Mat. Mekh., 1972, vol. 36, no.3, pp. 396-404. · Zbl 0257.34056
[97] Oziraner, A.S., Partial Asymptotic Stability and Instability, Prikl. Mat. Mekh., 1973, vol. 37, no.4, pp. 659-665. · Zbl 0295.34046
[98] Oziraner, A.S., Stability of Motion in Critical Cases, Prikl. Mat. Mekh., 1975, vol. 39, no.3, pp. 415-421. · Zbl 0344.34041
[99] Oziraner, A.S., Stability of Time-Varying Motion in First Approximation, Prikl. Mat. Mekh., 1976, vol. 40, no.3, pp. 424-430. · Zbl 0392.34032
[100] Oziraner, A.S., Partial Stability under Constant Perturbations, Prikl. Mat. Mekh., 1981, vol. 45, no.3, pp. 419-427. · Zbl 0498.70032
[101] Oziraner, A.S., Investigation of Partial Stability by Quadratic Forms, Prikl. Mat. Mekh., 1986, vol. 50, no.1, pp. 163-167. · Zbl 0618.34045
[102] Oziraner, A.S. and Rumyantsev, V.V., The Lyapunov Functions Method in Problems of Partial Stability of Motion, Prikl. Mat. Mekh., 1972, vol. 36, no.2, pp. 364-384. · Zbl 0272.34070
[103] Petrov, B.N., Rutkovskii, V.Yu., and Zemlyakov, S.D., Adaptivnoe koordinatno-parametricheskoe upravlenie nestatsionarnymi ob?ektami (Adaptive Coordinate-Parametric Control of Time-Varying Systems), Moscow: Nauka, 1980. · Zbl 0498.93002
[104] Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal?nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatlit, 1961.
[105] Prokop?ev, V.P., Partial Stability of Motion in a Critical Case of One Zero Root, Prikl. Mat. Mekh., 1975, vol. 39, no.3, pp. 422-426.
[106] Pyatnitskii, E.S., Design of Stabilization Systems for Programmed Motion of Nonlinear Systems, Avtom. Telemekh., 1993, no. 7, pp. 19-37.
[107] Roitenberg, Ya.N., Avtomaticheskoe upravlenie (Automatic Control), Moscow: Nauka, 1992. · Zbl 0786.49001
[108] Rubanovskii, V.N. and Rumyantsev, V.V., Stability of Motion of Complex Mechanical Systems, Usp. Mekh., 1979, vol. 2, no.2, pp. 53-79.
[109] Rumyantsev, V.V., Partial Stability of Motion, Vestn. Mosk. Gos. Univ., Mat. Mekh. Fiz. Astronom. Khim., 1957, no. 4, pp. 9-16.
[110] Rumyantsev, V.V., Stability of Equilibrium of a Body with a Liquid-filled Hollow, Dokl. Akad. Nauk SSSR, 1959, vol. 124, no.2, pp. 291-294.
[111] Rumyantsev, V.V., Stability of Rotational Motion of a Liquid-filled Solid, Prikl. Mat. Mekh., 1959, vol. 23, no.6, pp. 1057-1065.
[112] Rumyantsev, V.V., Stability of Motion of a Gyrostat, Prikl. Mat. Mekh., 1961, vol. 25, no.1, pp. 9-16. · Zbl 0100.36904
[113] Rumyantsev, V.V., Stability of Motion of Solids with Liquid-filled Hollows, Tr. II Vses. s?ezda po teor. prikl. mekh. (Proc. 2 All-Union Congress: Theoretical and Applied Mechanics), Moscow: Nauka, 1965, vol. 1, pp. 57-71.
[114] Rumyantsev, V.V., Ob ustoichivosti statsionarnykh dvizhenii sputnikov (Stability of Stationary Motion of Satellites), Moscow: Vychisl. Tsentr Akad. Nauk SSSR, 1967.
[115] Rumyantsev, V.V., Motion and Stability of an Elastic Body with a Liquid-filled Hollow, Prikl. Mat. Mekh., 1969, vol. 33, no.6, pp. 946-957.
[116] Rumyantsev, V.V., Optimal Stabilization of Control Systems, Prikl. Mat. Mekh., 1970, vol. 34, no.3, pp. 440-456. · Zbl 0215.59903
[117] Rumyantsev, V.V., Partial Asymptotic Stability and Instability of Motion, Prikl. Mat. Mekh., 1971, vol. 35, no.1, pp. 147-152. · Zbl 0265.34069
[118] Rumyantsev, V.V., Nekotorye zadachi ob ustoichivosti dvizheniya po otnosheniyu k chasti peremennykh. Mekhanika sploshnoi sredy i rodstvennye problemy analiza (Certain Problems in Partial Stability of Motion. Mechanics of Continuous Media and Allied Problems of Analysis), Moscow: Nauka, 1972.
[119] Rumyantsev, V.V., Optimal Partial Stabilization of Motion, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1993, no. 1, pp. 184-189.
[120] Rumyantsev, V.V. and Oziraner, A.S., Ustoichivost? i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh (Partial Stability and Stabilization of Motion), Moscow: Nauka, 1987. · Zbl 0626.70021
[121] Rutman, M.A., Boundedness of Solutions of Linear Differential and Differential Difference Equations, Tr. Odes. Gidromet. Inst., 1959, no. 20, pp. 3-7. · Zbl 0087.11702
[122] Savchenko, A.Ya. and Ignat?ev, A.O., Nekotorye zadachi ustoichivosti neavtonomnykh sistem (Certain Problems in the Stability of Nonautonomous Systems), Kiev: Naukova Dumka, 1989.
[123] Silakov, V.P. and Yudaev, G.S., Partial Stability of Difference Systems, Diff. Uravn., 1975, vol. 11, no.5, pp. 909-913.
[124] Sirazetdinov, T.K., Ustoichivost? sistem s raspredelennymi parametrami (Stability of Distributed-Parameter Systems), Moscow: Nauka, 1987. · Zbl 0631.93001
[125] Slyn?ko, V.I., Problems of Semistability of Motion, Prikl. Mekh., 2001, vol. 37, no.12, pp. 125-129.
[126] Smirnov, E.Ya. and Ermolina, M.V., Stabilizatsiya programmnykh dvizhenii mekhanicheskikh sistem po chasti peremennykh: voprosy kachestvennoi teorii differentsial?nykh uravnenii (Partial Stabilization of Programmed Motion of Mechanical Systems: Problems of the Qualitative Theory of Differential Equations), Novosibirsk: Nauka, 1988.
[127] Strogaya, G.V., Partial Stability of Decaying Systems under no Perturbations, Diff. Uravn., 1990, vol. 26, no.11, pp. 1949-1955.
[128] Tereki, I., Partial Stability of Solutions of Linear Autonomous Differential Difference Equations, Stud. Sci. Math. Hung., 1983, vol. 18, nos.2-4, pp. 143-152.
[129] Tereki, I. and Hatvani, L., Partial Stability and Convergence of Motion, Prikl. Mat. Mekh., 1981, vol. 45, no.3, pp. 428-435.
[130] Tereki, I. and Hatvani, L., Asymptotic Interruption under Viscous Friction, Prikl. Mat. Mekh., 1982, vol. 46, no.1, pp. 20-26.
[131] Tereki, I. and Hatvani, L., A Lyapunov Function of Mechanical Energy, Prikl. Mat. Mekh., 1985, vol. 49, no.6, pp. 894-899. · Zbl 0619.70018
[132] Tuan Bu, Partial Stability in First Approximation, Prikl. Mat. Mekh., 1980, vol. 44, no.2, pp. 211-220.
[133] Fradkov, A.L., Adaptivnoe upravlenie v slozhnykh sistemakh (Adaptive Control for Complex Systems), Moscow: Nauka, 1990. · Zbl 0732.93046
[134] Fradkov, A.L., Investigation of Physical Systems by Feedback, Avtom. Telemekh., 1999, no. 3, pp. 213-230. · Zbl 1273.93127
[135] Fradkov, A.L., Kiberneticheskaya fizika: printsipy i primery (Cybernetical Physics: Principles and Examples), St. Petersburg: Nauka, 2003.
[136] Furasov, V.D., Ustoichivost? dvizheniya, otsenki i stabilizatsiya (Stability of Motion, Estimation, and Stabilization), Moscow: Nauka, 1977.
[137] Furasov, V.D., Ustoichivost? i stabilizatsiya diskretnykh protsessov (Stability and Stabilization of Discrete Processes), Moscow: Nauka, 1982. · Zbl 0547.93047
[138] Khapaev, M.M., Usrednenie v teorii ustoichivosti, (Averaging in Stability Theory), Moscow: Nauka, 1986. · Zbl 0645.34044
[139] Hatvani, L., Certain Stability Criteria with Two Lyapunov Functions, Prikl, Mat. Mekh., 1975, vol. 39, no.1, pp. 172-177. (Errata: Prikl. Mat. Mekh., 1976, vol. 40, no. 2, pp. 251.)
[140] Hatvani, L., Application of Differential Inequalities in Stability Theory, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1975, no. 3, pp. 83-89. · Zbl 0308.34045
[141] Chudinov, K.M., Partial Stability of Linear Autonomous Hereditary Systems, Izv. Vuzov. Mat., 2004, vol. 48, no.6, pp. 72-78. · Zbl 1100.34529
[142] Sharov, V.F., Partial Stability and Stabilization of Stochastic Systems, Avtom. Telemekh., 1978, no. 11, pp. 63-71. · Zbl 0419.93087
[143] Shchennikov, V.N., Partial Stability of Differential Systems with Homogeneous Right Sides, Diff. Uravn., 1984, vol. 20, no.9, pp. 1645-1649. · Zbl 0582.34062
[144] Shchennikov, V.N., Partial Stability in the Critical Case of 2k Purely Imaginary Roots, in Differentsial?nye i integral?nye uravneniya: metody topologicheskoi dinamiki (Differential and Integral Equations: Methods of Topological Dynamics), Gor?kii: Gor?kovsk. Gos. Univ., 1985.
[145] Shchennikov, V.N., Metody sravneniya i metody Lyapunova (Comparison and Lyapunov Methods), Saransk: Mordovsk. Gos. Univ., 1990.
[146] Yudaev, G.S., Partial Stability, Diff. Uravn., 1975, vol. 11, no.6, pp. 1023-1029.
[147] Yudaev, G.S., Stability of Stochastic Differential Equations, Prikl. Mat. Mekh., 1977, vol. 41, vol. 3, pp. 430-435.
[148] Yurkov, A.V., Stabilization of Motion of Mechanical System by Indirect Partial Control, in Voprosy kachestvennoii teorii differents. uravnenii (Problems of Quatitative Theory of Differential Equations), Novosibirsk: Nauka, 1988, pp. 270-272.
[149] Yakubovich, V.A., Optimal Suppression of Interval Oscillations with a Given Output of a System, Dokl. Ross. Akad. Nauk, 1994, vol. 337, no.3, pp. 323-327. · Zbl 0847.93033
[150] Abed, E.H., Gover, R.E., Goldberg, A.J., and Wolk, S.I., Nonlinear and Stochastic Stability Problems in Gated Radar Range Trackers, Stoch. Theor. Contr. Lect. Notes. Control Int. Sci., 2002, vol. 280, pp. 1-17. · Zbl 1175.93233
[151] Akinyele, O., On Partial Stability of Differential Equations with Time Delay, Ann. Math. Pure Appl. (IV), 1979, vol. 121, pp. 351-372. · Zbl 0419.34075 · doi:10.1007/BF02412012
[152] Akinyele, O., Necessary Conditions for the Nonuniform Partial Stability for Delay Systems, Rend. Acc. Naz. del Lincei. Cl. Sci. Fis. Mat. Natur. (8), 1979, vol. 66, nos.3-4, pp. 509-515. · Zbl 0483.34050
[153] Akinyele, O., On Nonuniform Partial Stability and Perturbations for Delay Systems, Rend. Acc. Naz. del Lincei. Cl. Sci. Fis. Mat. Natur. (8)., 1980, vol. 67, nos.l?2, pp. 39-44. · Zbl 0471.34057
[154] Akinyele, O., On the Partial Stability of the Nonlinear Abstract Cauchy Problem, Riv. Mat. Univ. Parma. (IV), 1980, vol. 6, pp. 81-88. · Zbl 0466.34032
[155] Akinyele, O., On Partial Boundedness of Differential Equations with Time Delay, Riv. Mat. Univ. Parma. (IV), 1982, vol. 7, pp. 9-21. · Zbl 0502.34060
[156] Akinyele, O., Cone-Valued Lyapunov Functions and Stability of Impulsive Control Systems, Nonlin. Anal. TMA, 2000, vol. 39, no.2, pp. 247-259. · Zbl 0939.34057 · doi:10.1016/S0362-546X(98)00160-6
[157] Akulenko, L.D., Problems and Methods of Optimal Control, Dordrecht: Kluwer, 1994. · Zbl 0823.49001
[158] Angeli, D., Ingalls, B., Sontag, E.D., and Wang, Y., Uniform Global Asymptotic Stability of Differential Inclusions, J. Dynam. Control Syst., 2004, vol. 10, no.3, pp. 391-412. · Zbl 1053.34011 · doi:10.1023/B:JODS.0000034437.54937.7f
[159] Armellini, G., Sopra Un?equazione Differenziale Della Dinamica, Rend. Acc. Naz. del Lincei, 1935, vol. 21, nos.1-2, pp. 111-116. · Zbl 0011.20902
[160] Artstein, Z., Stabilization with Relaxed Controls, Nonlin. Anal. TMA, 1983, vol. 7, no.3, pp. 1163-1173. · Zbl 0525.93053 · doi:10.1016/0362-546X(83)90049-4
[161] Avakumovic, V.G., Sur l?Equation Differentielle de Thomas-Fermi, Bull. Inst. Math. Belgrade, 1947, vol. 1, pp. 101-113.
[162] Bajic, V.B., Partial Exponential Stability of Semistate Systems, Int. J. Control, 1986, vol. 44, no.5, pp. 1383-1394. · Zbl 0608.34057 · doi:10.1080/00207178608933674
[163] Bellman, R., Vector Liapunov Functions, SIAM J. Control, Ser. A, 1962, vol. 1, pp. 32-34. · Zbl 0144.10901
[164] Belloni, M. and Risito, C., On the Global Existence in the Future and Partial Boundedness of Motion of a Wide Class of Holonomic Scleronomic Systems, Rend. Mat. Appl. (VII), 1992, vol. 16, no.4, pp. 587-598. · Zbl 0880.70011
[165] Benner, P., Partial Stabilization of Generalized State-Space Systems using the Dick Function Method, PAMM, 2003, vol. 2, no.1, pp. 479-480. · Zbl 1201.65068 · doi:10.1002/pamm.200310222
[166] Benner, P., Castillo, M., and Quintana-Orti, E.S., Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems, J. Parallel. Distrib. Sci. Eng. Computing, 2004, vol. 1/2.
[167] Benner, P., Castillo, M., Quintana, E.S., and Hernandes, V., Parallel Partial Stabilizing Algorithms for Large Linear Control Systems, J. Supercomput., 2000, vol. 15, no.1, pp. 193-206. · Zbl 0953.68640 · doi:10.1023/A:1008108004247
[168] Bernfeld, S.R., Corduneanu, C., and Ignatyev, A.O., On the Stability of Invariant Sets of Functional Differential Equations, Nonlin. Anal. TMA, 2003, vol. 55, nos.4-6, pp. 641-656. · Zbl 1044.34027 · doi:10.1016/j.na.2003.08.002
[169] Blanchini, F., Set Invariance in Control, Automatica, 1999, vol. 35, no.11, pp. 1747-1767. · Zbl 0935.93005 · doi:10.1016/S0005-1098(99)00113-2
[170] Bondi, P., Fergola, P., Gambardella, L., and Tenneriello, C., Partial Stability of Large-Scale Systems, IEEE Trans. Automat. Control, 1978, vol. 24, no.1, pp. 94-97. · Zbl 0406.93047 · doi:10.1109/TAC.1979.1101930
[171] Bondi, P., Fergola, P., Gambardella, L., and Tenneriello, C., Partial Asymptotic Stability via Limiting Equations, Math. Meth. Appl. Sci., 1981, vol. 3, no.4, pp. 516-522. · Zbl 0494.34035 · doi:10.1002/mma.1670030136
[172] Brockett, R.W., Asymptotic Stability and Feedback Stabilization: Differential Geometric Control. Theory, Boston: Birkhauser, 1983. · Zbl 0528.93051
[173] Cai, W.X., The Connective Stability with respect to part of Variables of Dynamic Systems with Delay, J. Xiamen. Univ., Nat. Sci., 1984, vol. 23, no.3, pp. 291-299. · Zbl 0566.34048
[174] Cai, W.X., The Connective Stability with Respect to Part of Variables of Large-Scale Systems with Delay, J. Xiamen. Univ., Nat. Sci., 1987, vol. 26, no.3, pp. 277-285. · Zbl 0655.93009
[175] Campanini, R., On the Continuability and Partial Boundedness of the Solutions of Systems of Differential Equations, Bull. Unione Mat. Italy (VI), 1984, vol. 3, pp. 75-84. · Zbl 0538.34004
[176] Cantarelli, G., Criteria of Partial Boundedness for the Motion of Holonomic Scleronomic Dissipative Systems, Riv. Mat. Univ. Parma (V), 1995, vol. 4, pp. 69-78. · Zbl 0864.34025
[177] Cantarelli, G., Global Existence and Boundedness for Quasi-Variational Systems, Int. J. Math. Math. Sci., 1999, vol. 22, no.2, pp. 281-311. · Zbl 0942.34006 · doi:10.1155/S0161171299222818
[178] Cantarelli, G. and Risito, C., Criteri di Esistenza Globale e di Limitatezza per i Sistemi Olonomi Scleronomi, Ann. Math. Pure Appl. (IV), 1992, vol. 162, pp. 383-394. · Zbl 0768.70010 · doi:10.1007/BF01760017
[179] Cao, Q.G., Partial Stability of Linear Discrete Systems, J. Math. Res. Expo., 1989, vol. 9, no.4, pp. 541-545. · Zbl 0946.39500
[180] Cao, Q.G. and Xiong, K.Q., Partial Asymptotic Stability of Linear Time-varying Discrete Systems, Ann. Diff. Equat., 1993, vol. 9, no.2, pp. 141-149. · Zbl 0780.93083
[181] Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Berlin: Springer-Verlag, 1959. · Zbl 0082.07602
[182] Chellaboina, V. and Haddad, W.M., Teaching Time-varying Stability Theory using Autonomous Partial Stability Theory, Proc. IEEE Conf. Decision and Control, Orlando, 2001, pp. 3230-3235.
[183] Chellaboina, V. and Haddad, W.M., A Unification between Partial Stability and Stability Theory for Time-varying Systems, IEEE Control Systems Magazine, 2002, vol. 22, no.6, pp. 66-75. (Erratum: IEEE Control Syst. Magazine, 2003, vol. 23, no. 1. pp. 103.) · doi:10.1109/MCS.2002.1077786
[184] Corduneanu, C., Sur la stabilite partielle, Rev. Roumaine Math. Pures. Appl., 1964, vol. 9, no.3, pp. 229-236. · Zbl 0134.07104
[185] Corduneanu, C., Some Problems Concerning Partial Stability, Proc. Symp. Math. Meccanica Non-lineare Stabilita, 1970, New York: Academic, 1971, vol. 6, pp. 141-154.
[186] Corduneanu, C., On Partial Stability of Delay Systems, Ann. Pol. Math., 1974, vol. 29, pp. 357-362. · Zbl 0322.34055
[187] Djiaferis, T.E., Partial Stability Preserving Maps and Stabilization, Proc. IEEE Conf. Decision Control, 2003, pp. 2490-2495.
[188] Dragan, V. and Halanay, A., Partial Stability for Singularly Perturbed Systems, Proc. Workshop: Diff. Equations and Their Contr., 1983, pp. 36-45. · Zbl 0509.34059
[189] Edwards, H., Lin, Y., and Wang, Y., On Input-to-State Stability of Time-varying Nonlinear Systems, Proc. IEEE Conf. Decision and Control, Sydney, 2000, pp. 3501-3506.
[190] Efimov, D.V., A Universal Formula for Output Asymptotic Stabilization, Proc. 15 IFAC World Congr., Barselona, Spain, 2002.
[191] El-Gohary, A., Optimal Stabilization of the Rotational Motion of a Rigid Body with the Help of Rotors, Int. J. Nonlin. Mech., 2000, vol. 35, no.3, pp. 393-403. · Zbl 1068.70506 · doi:10.1016/S0020-7462(99)00025-6
[192] Esclangon, E., Nouvelles Recherches sur les Fonctions Quasiperiodiques, Ann. Obs. Bordeaux, 1917, vol. 16, pp. 51-226.
[193] Fergola, P. and Moauro, V., On Partial Stability, Ricerche Mat., 1970, vol. 19, no.2, pp. 185-207. · Zbl 0228.34035
[194] Fergola, P. and Tenneriello, C., Partial Stability of Composite Systems with Unstable Subsystems, Large-Scale Syst., 1983, vol. 4, pp. 101-105. · Zbl 0512.93009
[195] Fergola, P. and Tenneriello, C., Lotka-Volterra Models: Partial Stability and Partial Ultimate Boundedness, Biomath. Related Comput. Probl., 1988, pp. 283-294. · Zbl 0658.92017
[196] Fradkov, A.L., Exploring Nonlinearity by Feedback, Physica D, 1999, vol. 128, nos.2-4, pp. 159-168. · Zbl 0939.93511 · doi:10.1016/S0167-2789(98)00322-4
[197] Fradkov, A.L., Physics and Control: Exploring Physical Systems by Feedback, Prep. V IFAC Symp. Nonlinear Control Systems, 2001, vol. 5, pp. 1503-1509.
[198] Fradkov, A.L., Miroshnik, I.V., and Nikiforov, V.O., Nonlinear and Adaptive Control of Complex Systems, Dordrecht: Kluwer, 1999. · Zbl 0934.93002
[199] Fradkov, A.L. and Pogromsky, A.Yu., Introduction to Control of Oscillations and Chaos, Singapure: World Scientific, 1998. · Zbl 0945.93003
[200] Ge, Z.M. and Chen, Y.S., Synchronization of Undirectional Coupled Chaotic Systems via Partial Stability, Chaos, Solitons, and Fractals, 2004, vol. 21, no.1, pp. 101-111. · Zbl 1048.37027 · doi:10.1016/j.chaos.2003.10.004
[201] Geluk, J.L., Note on a Theorem of Avakumovic, Proc. Am.Math. Soc., 1991, vol. 112, no.2, pp. 429-431. · Zbl 0722.34045
[202] Guo, Y.X., Partial Stability for Nonlinear Time-varying Dynamical Systems, Ann. Diff. Equat., 1992, vol. 8, no.3, pp. 276-283. · Zbl 0767.34034
[203] Haddad, W.M., Chellaboina, V., and Nersesov, S.G., A Unification between Partial Stability of State-dependent Impulsive Systems and Stability Theory for Time-dependent Impulsive Systems, Int. J. Hybrid Syst., 2002, vol. 2, nos.1-2, pp. 155-168.
[204] Haddad, W.M., Chellaboina, V., and Nersesov, S.G., A Unification between Partial stability of State-dependent Impulsive Systems and Stability Theory for Time-dependent Impulsive Systems, Proc. Am. Control Conf., Denver, 2003, pp. 4004-4009.
[205] Haddad, W.M., Chellaboina, V., and Oh, J.H., Linear Controller Analysis and Design for Systems with Input Hysteresis and Nonlinearities, J. Franklin Inst., 2003, vol. 340, no.5, pp. 371-390. · Zbl 1054.93022 · doi:10.1016/j.jfranklin.2003.08.002
[206] Hagedorn, P., Steady Motions in Controlled Gyrostat Systems, Ing. Arch., 1982, vol. 52, no.2, pp. 183-204. · Zbl 0503.70003 · doi:10.1007/BF00535312
[207] Hahn, W., Stability of Motion, Berlin: Springer-Verlag, 1967. · Zbl 0189.38503
[208] Halanay, A., Differential Equations: Stability, Oscillations, Time Lags, New York: Academic, 1966. · Zbl 0144.08701
[209] Hale, J.K., Theory of Functional Differential Equations, New York: Springer-Verlag, 1977. Translated under the title Teoriya funktsional?no-differentsial?nykh uravnenii, Moscow: Mir, 1984.
[210] Hatvani, L., On Partial Asymptotic Stability and Instability. I. Autonomous Systems; II. The Method of Limiting Equations, Acta Sci. Math., 1983, vol. 45, pp. 219-231; vol. 46, pp. 143-156. · Zbl 0524.34057
[211] Hatvani, L., On the Asymptotic Stability to Nondecreasing Lyapunov Functions, Nonlin. Anal. TMA, 1984, vol. 8, no.1, pp. 67-77. · Zbl 0534.34054 · doi:10.1016/0362-546X(84)90028-2
[212] Hatvani, L., On Partial Asymptotic Stability and Instability. III. Energy-like Ljapunov Functions, Acta Sci. Math., 1985, vol. 49, pp. 157-167. · Zbl 0633.34042
[213] Hatvani, L., On Partial Asymptotic Stability by the Method of Limiting Equations, Ann. Math. Pura Appl. (IV), 1985, vol. 139, pp. 65-82. · Zbl 0571.34039 · doi:10.1007/BF01766850
[214] Hatvani, L., On the Stability of the Solutions of Ordinary Differential Equations with Mechanical Applications, Alkalmaz. Mat. Lapok., 1991, vol. 15, no.1/2, pp. 1-90. · Zbl 0769.34040
[215] Hatvani, L., On the Armellini-Sansone-Tonelli Theorem, Mem. Di_. Equat. Math. Phys., 1997, vol. 12, pp. 76-81. · Zbl 0994.34036
[216] Hatvani, L. and Terjeki, I., Stability Properties of the Equilibrium under the Influence of Unbounded Damping, Acta Sci. Math., 1985, vol. 48, nos.1-4, pp. 187-200.
[217] Havre, K. and Skogestad, S., Input/output Selection and Partial Control, Proc. 13 IFAC Triennial World Congr., San Francisco, 1996, vol. M, pp. 181-186.
[218] Huang, L., A Discussion on Some Problems of Lyapunov Matrix Equation for Partial Stability, J. Math. Res. Expo., 1990, vol. 10, no.2, pp. 195-198. · Zbl 0794.93078
[219] Ignatyev, A.O., On the Partial Equiasymptotic Stability of Functional-Differential Equations, J. Math. Anal. Appl., 2002, vol. 268, no.2, pp. 615-628. · Zbl 1007.34071 · doi:10.1006/jmaa.2001.7835
[220] Ingalls, B.P., Comparisons of Notions of Stability for Nonlinear Control Systems with Outputs, PhD Dissertation, Rutgers University, New Brunswick, 2001.
[221] Ingalls, B.P., Sontag, E.D., and Wang, Y., Measurement to Error Stability: A Notion of Partial Detectability for Nonlinear Systems, Proc. IEEE Conf. Decision and Control, Las Vegas, 2002, pp. 3946-3951.
[222] Ingalls, B. and Wang, Y., On Input-to-Output Stability for Systems not Uniformly Bounded, Prep. V IFAC Symp. Nonlinear Control Systems, 2001, vol. 5, pp. 1503-1509.
[223] Isidori, A., Nonlinear Control Systems II, London: Springer-Verlag, 1999. · Zbl 0931.93005
[224] Jian, J.G. and Liao, X.X., Partial Exponential Stability of Nonlinear Time-varying Large-Scale Systems, Nonlin. Anal. TMA, 2004, vol. 59, no.5, pp. 789-800. · Zbl 1059.34032
[225] Kertesz, V., Partial Stability Investigations of Differential Equational of Second Order, Comput. Math. Appl., 1991, vol. 21, no.1, pp. 95-102. · Zbl 0726.34042 · doi:10.1016/0898-1221(91)90234-U
[226] Khalil, H.K., Nonlinear Systems, Upper Saddle River: Prentice Hall, 1996.
[227] Khapaev, M.M., Usrednenie v teorii ustoichivosti (Averaging in Stability Theory), Moscow: Nauka, 1986. · Zbl 0645.34044
[228] Kolesnichenko, O. and Shiriaev, A.S., Partial Stabilization of Underactuated Euler-Lagrange Systems via a Class of Feedback Transformations, Syst. Control Lett., 2002, vol. 45, no.2, pp. 299-305. · Zbl 0987.93065 · doi:10.1016/S0167-6911(01)00170-0
[229] Kothare, M.V., Shinnar, R., Rinard, I., and Morari, M., On Defining the Partial Control Problem: Concepts and Examples, Proc. Am. Control Conf., Philadelphia, 1998, pp. 2103-2107; AIChE J., 2000, vol. 46, no. 12, pp. 2456-2474.
[230] Kovalev, A.M., Control and Stabilization Problems with Respect to Part of Variables, ZAMM, 1994, vol. 74, no.7, pp. 59-60.
[231] Krichman, M., Sontag, E.D., and Wang, Y., Input-Output-to-State Stability, SIAM J. Contr. Optim., 2000, vol. 39, no.6, pp. 1874-1928. · Zbl 1005.93044 · doi:10.1137/S0363012999365352
[232] Krstic, M. and Deng, H., Stabilization of Nonlinear Uncertain Systems, London: Springer-Verlag, 1998.
[233] Kundur, P., Paserba, J., Ajjarapu, V., et al., Definition and Classification of Power Systems Stability, IEEE Trans. Power Systems, 2004, vol. 19, no.3, pp. 1387-1401. · doi:10.1109/TPWRS.2004.825981
[234] Lakshmikantham, V. and Liu, X.Z., Stability Analysis in Terms of Two Measures, Singapure: World Scientific, 1993. · Zbl 0797.34056
[235] Lakshmikantham, V. and Salvadori, L., On Massera-type Converse Theorems in Terms of Two Different Measures, Boll. Unione Mat. Ital. Ser. A, 1976, vol. 13, no.2, pp. 293-301. · Zbl 0351.34030
[236] La Salle, J.P. and Rath, R.J., Eventual Stability, Proc. 2 IFAC Triennial World Congr., 1963, vol. 1, pp. 556-560.
[237] Li, W.J. and Duan, K.C., Partial Stability and Boundedness of Solutions to Retarded Functional-Differential Equations, J. Xinjiang Univ., Nat. Sci., 1993, vol. 10, no.4, pp. 31-33. · Zbl 1056.34524
[238] Liao, X.X. and Li, J., Robust Interval Stability, Persistence, and Partial Stability on Lotka-Volterra Systems with Time-Delay, Appl. Math. Comput., 1996, vol. 75, nos.2-3, pp. 103-115. · Zbl 0857.34067 · doi:10.1016/S0096-3003(96)90049-1
[239] Liao, X.X. and Wu, W.H., Necessary and Sufficient Conditions for the Partial Stability of Linear Dynamical Systems, Chin. Sci. Bull., 1990, vol. 35, no.11, pp. 899-903. · Zbl 0744.34049
[240] Lin, X.Y., On Converses to the Partial Stability Theorems for Difference Equations, Pure Appl. Math., 1992, vol. 8, no.1, pp. 32-36. · Zbl 0856.39005
[241] Lin, Y., Lyapunov Functions Techniques for Stabilization, PhD Dissertation, Rutgers University, New Brunswick, 1992.
[242] Lin, Y., Sontag, E.D., and Wang, Y., A Smooth Converse Lyapunov Theorem for Robust Stability, SIAM J. Contr. Optim., 1996, vol. 34, no.1, pp. 124-160. · Zbl 0856.93070 · doi:10.1137/S0363012993259981
[243] Luyben, B.L., Tyrens, B.D., and Luyben, M.L., Plantwide Process Control, New York: McGraw-Hill, 1999.
[244] Magnus, K. Kreisel, Theorie und Anwendungen, Berlin: Springer-Verlag, 1971.
[245] Mahony, R., Mareels, I.M., Campion, G., and Bastin, G., Output Stabilization of Square Nonlinear Systems, Automatica, 1997, vol. 33, no.8, pp. 1571-1577. · Zbl 0882.93070 · doi:10.1016/S0005-1098(97)00052-6
[246] Mao, X.R., Some Contributions to Stochastic Asymptotic Stability and Boundedness via Multiple Lyapunov Functions, J. Math. Anal. Appl., 2001, vol. 260, no.2, pp. 325-340. · Zbl 0983.60055 · doi:10.1006/jmaa.2001.7451
[247] Martynyuk, A.A., Stability by Liapunov?s Matrix Function Method with Applications, New York: Marcel Dekker, 1998. · Zbl 0907.34034
[248] Meirovitch, L., Liapunov Stability Analysis of Hybrid Dynamical Systems in the Neighbourhood of Nontrivial Equilibrium, Ibid, 1974, vol. 12, no.7, pp. 889-898. · Zbl 0293.70019
[249] Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability and Boundedness of Discontinuous Dynamical Systems, Nonlin. Studies, 2002, vol. 9, no.3, pp. 225-247. · Zbl 1032.34052
[250] Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability of Systems with Applications to Discrete Events Systems, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.
[251] Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability of Discontinuous Dynamical Systems, Proc. Am. Contr. Conf., Anchorage, 2002, pp. 74-79. · Zbl 1032.34052
[252] Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability and Boundedness of General Dynamical Systems on Metric Spaces, Nonlin. Anal. TMA, 2003, vol. 52, no.4, pp. 1295-1316. · Zbl 1035.37008 · doi:10.1016/S0362-546X(02)00167-0
[253] Michel, A.N. and Sun, Y., Partial Stability of General Dynamical Systems under Arbitrary Initial z-Perturbations, Int. J. Hybrid Syst., 2002, vol. 2, nos.1-2, pp. 57-92.
[254] Miki, K., Partial Integral Stability Theorems by Comparison Principle, Res. Rept. Akita Tech. Coll., 1990, vol. 25, pp. 84-89.
[255] Miki, K., Masamichi, A., and Shoichi, S., On the Partial Total Stability and Partially Total Boundedness of a System of Ordinary Differential Equations, Res. Rept. Akita Tech. Coll., 1985, vol. 20, pp. 105-109.
[256] Miroshnik, I.V., Partial Stability and Geometric Problems of Nonlinear Control, Proc. 15 IFAC Triennial World Congress, Barselona, 2002. · Zbl 1107.34334
[257] Miroshnik, I.V., Attractors and Partial Stability of Nonlinear Dynamical Systems, Automatica, 2004, vol. 40, no.3, pp. 473-480. · Zbl 1041.93043 · doi:10.1016/j.automatica.2003.10.016
[258] Molchanov, A.P., Michel, A.N., and Sun, Y., Converse Theorems of the Principal Lyapunov Results for Partial Stability of General Dynamical Systems on a Metric Space, Nonlin. Stud., 2003, vol. 10, no.2, pp. 113-134. · Zbl 1057.37012
[259] Muller, P.S., Stabilitat und Matrizen, Berlin: Springer-Verlag, 1977.
[260] Muller, P.S., Zum Problem der Partiellen Asymptotichen Stabilitat, Fest. zum 70 Gelebr. von Herrn Prof. Dr. K. Magnus, TU Munchen, 1982, pp. 237-268.
[261] Muller, P.S., Kriterien fur Untersuchung der Partiellen Asymptotischen Stabilitas, ZAMM, 1984, vol. 64, no.4, pp. 71-72.
[262] Muller, P.S., Stability and Optimal Control of Nonlinear Descriptor Systems: A Survey, Int. J. Appl. Math. Comput. Sci., 1998, vol. 8, no.2, pp. 269-286. · Zbl 0910.93047
[263] Muresan, M., On Partial Stability of Differential Inclusions, Proc. Int. Conf. Diff. Equations, Barcelona, 1991, Perello C., Ed., Singapure: World Scientific, 1993, pp. 778-780. · Zbl 0938.34504
[264] Pachpatte, B.G., Partial Stability of Solutions of Difference Equations, Proc. Nat. Acad. Sci., India, Sect. A, 1973, vol. A3, pp. 235-238. · Zbl 0302.39002
[265] Pascal, M., La Stabilite d?Attitude dun Satellite muni de Panneaux Solares, Ibid, 1978, vol. 5, no.10, pp. 817-844. · Zbl 0402.70023
[266] Peiffer, K., La Methode de Liapunoff Appliquée á I Edúte de la StabilitePartielle, Université Catholique de Louvain, Faculté des sciences. 1968.
[267] Peiffer, K. and Rouche, N., Lyapounov?s Second Method applied to Partial Stability, J. Mecanique, 1969, vol. 8, no.2, pp. 323-334. · Zbl 0183.36701
[268] Peng, L.P., Strong Stability to Part of Variables in Systems with Impulse Effect, J. Beijing Univ. Aeron. Astron., 2001, vol. 27, no.3, pp. 365-369.
[269] Peng, S.T. and Chen, C.K., Estimation of the Partial Stability Region of a Class of Robust Controllers with Input Constraints, J. Franklin Inst., 1998, vol. 335, no.7, pp. 1271-1281. · Zbl 1049.93559 · doi:10.1016/S0016-0032(97)00072-0
[270] Phillis, Y., Y-Stability and Stabilizability in the Mean of Discrete-Time Stochastic Systems, Int. J. Control, 1984, vol. 40, no.1, pp. 149-160. · Zbl 0552.93062 · doi:10.1080/00207178408933264
[271] Pico-Marco, E. and Pico, J., Partial Stability for Specific Growth Rate Control in Biotechnological Feed-Batch Processes, Proc. IEEE Conf. Control Appl., 2003, pp. 724-728.
[272] Potcovaru, G., On the Partial Stability of Dynamical Systems with Random Parameters, Ann. Univ. Bucur. Math., 1999, vol. 48, no.2, pp. 163-168. · Zbl 0969.43009
[273] Prodi, G., Un? Osservazione Sugl? Integrali Dell? Equazione ÿ + A(x)y = 0 Net Caso A(x) ? + ? per x ? + ?, Rend. Acc. Naz. del Lincei, 1950, vol. 8, pp. 462-464. · Zbl 0037.34102
[274] Risito, C., Sulla Stabilita Asintotica Parziale, Ann. Math. Pura Appl., 1970, vol. 84, pp. 279-292. · Zbl 0213.10602 · doi:10.1007/BF02413656
[275] Risito, C., Metodi per lo Studio Della Stabilita di Sistemi con Integrali Primi Noti, Ann. Math. Pura Appl., 1976, vol. 107, pp. 49-94. · Zbl 0341.34039 · doi:10.1007/BF02416468
[276] Rokni Lamooki, G.R. and Townley, S.B., Partial Stability in Back-Stepping and Adaptive Control, Proc. Int. Conf. Methods Models in Autom. and Robotics, Miedzyzdroje, 2003, pp. 491-496.
[277] Rouche, N., Habets, P., and LaLoy, M., Stability Theory by Liapunov?s Direct Method, NewYork: Springer-Verlag, 1977. Translated under the title Pryamoi metod Lyapunova v teorii ustoichivosti, Moscow: Mir, 1980. · Zbl 0364.34022
[278] Rouche, N. and Peiffer, K., Le Theoreme de Lagrange-Dirichle et la Deuxieme Methode de Lyapunoff, Ann. Soc. Scient. Bruxelle. Ser. I, 1967, vol. 81, no.1, pp. 19-33.
[279] Routh, J.E., A Treatise on the Stability of a Given State of Motion, London: Macmillan, 1877.
[280] Rumyantsev, V.V., On the Stability to Part of Variables, Symp. Math. Meccanica Nonlineare Stability, New York: Academic, 1971, vol. 6, pp. 243-265. · Zbl 0226.34047
[281] Russinov, I.K., Partial Asymptotic Stability and Instability of Nonautonomous Systems, Nauchni Tr., Plovdivski Univ. Mat., 1988, vol. 26, no.3, pp. 67-73.
[282] Russinov, I.K., Integral Stability to Part of Variables and Perturbing Lyapunov Functions, Nauchni Tr., Plovdivski Univ., Mat., 1994, vol. 31, no.3, pp. 83-87. · Zbl 0855.34060
[283] Salvadori, L., Sul Problema Della Stabilita Asimptotica, Rend. Acc. Naz. del Lincei, 1972, vol. 53, nos.1-2, pp. 35-38.
[284] Salvadori, L., Some Contributions to Asymptotic Stability Theory, Ann. Soc. Scient. Bruxelle. Ser. 1, 1974, vol. 88, no.2, pp. 183-194. · Zbl 0286.34087
[285] Sansone, G., Sopra il Comportamento Asintotico delle Soluzioni di un? Equazione Differenziale della Dinamica, Scritti Math. offerti a Luigi Berzolari, Pavia, 1936, pp. 385-403. · JFM 62.1273.04
[286] Sansone, G., Equazioni Differenziali nel Campo Reale, Bologna: Zanichelli, 1949.
[287] Scott, F.J., New Partial Asymptotic Stability Results for Nonlinear Ordinary Differential Equations, Pacific J. Math., 1977, vol. 72, no.2, pp. 523-535. · Zbl 0366.34040
[288] Scott, F.J., On a Partial Asymptotic Stability Theorem of Willett and Wong, J. Math. Anal. Appl., 1978, vol. 63, no.2, pp. 416-420. · Zbl 0383.34042 · doi:10.1016/0022-247X(78)90087-2
[289] Sepulchre, R., Jankovic, M., and Kokotovic, P.V., Constructive Nonlinear Control, London: Springer-Verlag, 1997.
[290] Shen, J.H. and Du, X.T., Partial Exponential Stability of Large-Scale Nonautonomous Discrete Systems, Acta Sci. Nat. Univ. Norm. Hunan., 1995, vol. 18, no.3, pp. 16-21. · Zbl 0843.93064
[291] Shen, Y.Y., Partial Stability and Unstability of Ito Stochastic Systems, J. Stangdong Coll. Oceanol., 1982, vol. 12, no.4, pp. 69-76. · Zbl 0515.93068
[292] Shiriaev, A.S., The Notion of V-Detectability and Stabilization of Invariant Sets of Nonlinear Systems, Syst. Control Lett., 2000, vol. 39, no.5, pp. 327-338. · Zbl 0948.93047 · doi:10.1016/S0167-6911(99)00112-7
[293] Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Cascaded Nonlinear Systems, Proc. IEEE Conf. Decision Control, Phoenix, 1999, pp. 1296-1301.
[294] Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Nonlinear Nonaffine Systems, Automatica, 2000, vol. 36, no.11, pp. 1709-1715. · Zbl 0966.93090 · doi:10.1016/S0005-1098(00)00077-7
[295] Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Nonlinear Systems with Applications to Control of Oscillations, Int. J. Robust Nonlin. Control, 2001, vol. 11, no.3, pp. 215-240. · Zbl 0979.93087 · doi:10.1002/rnc.568
[296] Shoichi, S., On the Partial Uniformly Integral Stability of Solutions of Ordinary Differential Equations, Res. Rept. Akita Tech. Coll., 1990, vol. 25, pp. 78-83.
[297] Shoichi, S., Miki, K., and Masamichi, A., Partial Stability Theorems by Comparison Principle, Res. Rept. Akita Tech. Coll., 1982, vol. 17, pp. 95-99.
[298] Shu, W.H., On Partial Stability of Functional-Differential Equations with Delay, J. Cent. China Norm. Univ., Nat. Sci., 1996, vol. 30, no.2, pp. 135-138. · Zbl 0907.34059
[299] Simenov, P.S. and Bainov, D.D., Stability to Part of Variables in Systems with Impulse Effect, J. Math. Anal. Appl., 1986, vol. 117, no.1, pp. 247-263; 1987, vol. 124, no. 2, pp. 547-560. · Zbl 0588.34044 · doi:10.1016/0022-247X(86)90259-3
[300] Sontag, E.D., A Universal Construction of Artstein?s Theorem on Nonlinear Stabilization, Syst. Control Lett., 1989, vol. 13, no.2, pp. 117-123. · Zbl 0684.93063 · doi:10.1016/0167-6911(89)90028-5
[301] Sontag, E.D., Mathematical Control Theory: Deterministic Finite Dimensional Systems, NewYork: Springer-Verlag, 1998. · Zbl 0945.93001
[302] Sontag, E.D., The ISS philosophy as a Unifying Framework for Stability Behavior, in Nonlinear Control in The Year Isidori, A., Lamnabhi-Lagarrigue, F., and Respondek, W., Eds., Berlin: Springer-Verlag, 2000, vol. 2, pp. 443-468.
[303] Sontag, E.D., Input-to-State Stability and Related Notions, Proc. Symp. Chemical Process Contr. VI, Tueson, 2001, pp. 109-120.
[304] Sontag, E.D. and Wang, Y., A Notion of Input-to-Output Stability, Proc. Europ. Control Conf., Brussels, 1997, Paper WE-E-A2. · Zbl 0968.93076
[305] Sontag, E.D. and Wang, Y., Output-to-State Stability and Detectability of Nonlinear Systems, Syst. Control Lett., 1997, vol. 29, nos.4-5, pp. 279-290. · Zbl 0901.93062 · doi:10.1016/S0167-6911(97)90013-X
[306] Sontag, E.D. and Wang, Y., Notions of Input-to-Output Stability, Syst. Control Lett., 1999, vol. 38, nos.4-5, pp. 235-248. · Zbl 0985.93051 · doi:10.1016/S0167-6911(99)00070-5
[307] Sontag, E.D. and Wang, Y., Lyapunov Characterizations of Input-to-Output Stability, SIAM J. Control Optim., 2001, vol. 39, no.1, pp. 226-249. · Zbl 0968.93076 · doi:10.1137/S0363012999350213
[308] Sun, Y. and Michel, A.N., Partial Stability of General Dynamical Systems under Arbitrary Initial z-Perturbations, Tranc. IEEE Conf. Decision Control, Las Vegas, Nevada, 2002, pp. 2663-2668.
[309] Sun, Y. and Michel, A.N., Partial Stability and Boundedness of Discontinuous Dynamical Systems under Arbitrary Initial z-Perturbations, Int. J. Hybrid Syst., 2002, vol. 2, no.3, pp. 261-288.
[310] Sun, Y., Molchanov, A.P., and Michel, A.N., Partial Stability of Dynamical Systems, Proc. 15 Int. Symp. Math. Theory Networks Syst., Univ. Notre Dame, 2002. · Zbl 1032.34052
[311] Talpalary, P. and Stefancu, D., On Partial Stability of Multivalued Differential Equations, Bull. Inst. Politech. Iasi. Ser. I, 1987, vol. 33, nos.1-4, pp. 41-46.
[312] Tang, S.Y. and Xi, Y.N., Robust Interval Stability and Partial Stability of Kolmogorov Systems with Time Delay, J. Math., Wuhan Univ., 2000, vol. 20, no.2, pp. 180-184. · Zbl 0954.34067
[313] Teel, A. and Praly, L., A Smooth Lyapunov Function from a Class of K L-estimates Involving Two Positive Semidefinite Functions, ESAIM: Contr., Optimiz. Calculus Variat., 2000, vol. 5, pp. 313-367. · Zbl 0953.34042 · doi:10.1051/cocv:2000113
[314] Tian, X.G., An Extension of a Stability Theorem on Discrete Systems and the Lyapunov Function to Partial Stability, Acta Math. Sin., 1993, vol. 36, no.5, pp. 676-681. · Zbl 0801.93055
[315] Tonelli, L., Estratto di Lettera al Prof. G. Sansone, Scritti Math. offerti a Luigi Berzolari, Pavia, 1936, pp. 404-405.
[316] Tsiotras, P. and Schleicher, A., Detumbling and Partial Attitude Stabilization of a Rigid Spacecraft under Actuator Failure, AIAA Guidance, Navigat. Control Conf., Denver, Colorado, 2000, AIAA Paper 00-4044.
[317] Tsiotras, P. and Wilson, B.C., Zero-and Low-Bias Control Design for Active Magnetic Bearings, IEEE Tranc. Cont rol Syst. Tech., 2003, vol. 11, no.6, pp. 889-904. · doi:10.1109/TCST.2003.819593
[318] Vannelli, A. and Vidyasagar, M., Theory of Partial Stability: Theorems, Converse Theorems, and Maximal Lyapunov Functions, Proc. Annual Southeast Symp., Piscataway, 1980, pp. 16-20.
[319] Vorotnikov, V.I., Ustoi?chivost? dinamicheskikh sistem po otnosheniyu k chasti peremennykh (Stability of Dynamic Systems Relative to Part of Variables), Moscow: Nauka, 1991. · Zbl 0734.93063
[320] Vorotnikov, V.I., Partial Stability, Stabilization, and Control: Some Recent results, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.
[321] Wada, T., Ohta, Y., Ikeda, M., and Siljak, D.D., Parametric Absolute Stability of Lur?e Systems, Proc. IEEE Conf. Decision Control, New Orleans, 1995, p. 1449-1454.
[322] Wang, P.K.C., Stability Analysis of Elastic and Aeroelastic Systems via Lyapunov?s Direct Method, J. Franklin Inst., 1966, vol. 281, no.1, pp. 51-72. · Zbl 0148.20102 · doi:10.1016/0016-0032(66)90067-6
[323] Weiss, L. and Infante, E.F., Finite-Time Stability under Perturbing Forces and on Product Spaces, IEEE Tranc. Autom. Control, 1967, vol. 12, no.1, pp. 54-59. · Zbl 0168.33903 · doi:10.1109/TAC.1967.1098483
[324] Willems, J.L., A Partial Stability Approach to the Problem of Transient Power System Stability, Int. J. Control, 1974, vol. 19, no.1, pp. 1-14. · Zbl 0278.93025 · doi:10.1080/00207177408932606
[325] Wilson, F.W., Jr., Smoothing Derivatives of Functions and Applications, Trans. Amer. Math. Soc., 1969, vol. 139, pp. 413-428. · Zbl 0175.20203 · doi:10.1090/S0002-9947-1969-0251747-9
[326] Wiman, A., Ueber eine Stabilitatsfrage in der Theorie der linearen Differentialgleichungen, Acta Math., 1936, vol. 66, pp. 121-145. · Zbl 0014.01902 · doi:10.1007/BF02546518
[327] Wu, C.W. and Chua, L.O., A Unified Framework for Synchronization and Control of Dynamical Systems, Int. J. Bifurcat. Chaos, 1994, vol. 4, no.4, pp. 979-998. · Zbl 0875.93445 · doi:10.1142/S0218127494000691
[328] Xiao, H.M. and Liu, Y.Q., Partial Exponential Stability of Large-Scale Systems, Math. Appl., 1990, vol. 3, no.2, pp. 65-70. · Zbl 0895.34045
[329] Xiao, H.M., Liu, Y.P., and Hu, Y.M., The Partial Boundedness of Neutral Functional Systems and Their Perturbation Systems, Adv. Model. Simul., 1992, vol. 30, no.2, pp. 5-15. · Zbl 0783.93098
[330] Xiong, K.Q. and Cao, Q.G., On the Partial Stability of a Linear System and Control System, Ann. Diff. Equat., 1989, vol. 5, no.1, pp. 87-97. · Zbl 0676.34032
[331] Yang, T., Impulsive Control Theory, Berlin: Springer-Verlag, 2001. · Zbl 0996.93003
[332] Yoshizawa, T., Stability Theory by Liapounov?s Second Method, Tokyo: Math. Soc. Japan, 1966. · Zbl 0144.10802
[333] Yu, G.D., On the Partial Stability of Impulsive Differential Equations, Ann. Diff. Equat., 1998, vol. 14, no.2, pp. 407-412. · Zbl 0967.34048
[334] Zames, G., On the Input-Output Stability of Time-varying Nonlinear Feedback Systems. I, II, IEEE Trans. Automat Control, 1966, vol. 11, no.2, pp. 228-238; no. 3, pp. 465-477. · doi:10.1109/TAC.1966.1098316
[335] Zhao, J.X., On Partial Asymptotic Stability and Limit Equations, J. Nanjing Univ. Math. Biquart., 1990, vol. 7, no.1, pp. 100-108. · Zbl 0733.34057
[336] Zhu, H.P. and Mei, F.X., On the Stability of Nonholonomic Mechanical Systems to Part of Variables, Chin. J. Appl. Math. Mech., 1995, vol. 16, no.3, pp. 225-233.
[337] Zubov, S.V., Rated Stability, Proc. 1 Int. Conf. Controlled Oscillations and Chaos, St.-Petersburg, 1997, vol. 1, pp. 170-171.
[338] Zuyev, A.L., On Brockett?s Condition for Smooth Stabilization by Part of Variables, Proc. Eur. Control Conf., Karlsruhe, 1999.
[339] Zuyev, A.L., On Partial Stabilization of Nonlinear Autonomous Systems: Sufficient Conditions and Examples, Proc. Eur. Control Conf., Porte, 2001. pp. 1918-1922.
[340] Zuyev, A.L., Partial Stabilization of a Rigid Body by Several Elastic Beams, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.
[341] Zuyev, A.L., Partial Asymptotic Stability and Stabilization of Nonlinear Abstract Differential Equations, Proc. IEEE Conf. Decision Control, Maui, 2003, pp. 1321-1326.
[342] Zuyev, A.L., On Partial Stabilization of a System of Euler-Bernoulli Beam Equations, The Abdus Salam Int. Center for Theor. Phys., Trieste, 2003.
[343] Zuyev, A.L., On Partial Asymptotic Stabilization of Nonlinear Distributed-Parameter Systems, Automatica, 2005, vol. 41, no.1, pp. 1-10. · Zbl 1067.93037 · doi:10.1016/S0005-1098(04)00240-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.