zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Dissipative dynamical systems. II: Linear systems with quadratic supply rates. (English) Zbl 0252.93003

MSC:
93A10General systems
70GxxGeneral models, approaches, and methods for dynamical systems
94C10Switching theory, application of Boolean algebra; Boolean functions
References:
[1]Brockett, R. W., Finite Dimensional Linear Systems. New York: Wiley 1970.
[2]Kalman, R. E., P. L. Falb, & M. A. Arbib, Topics in Mathematical System Theory. New York: McGraw-Hill 1969.
[3]Willems, J. C., & S. K. Mitter, Controllability, observability, pole allocation, and state reconstruction. IEEE Transactions on Automatic Control AC-16, 582-595, December (1971). (Special issue on the Linear-Quadratic-Gaussian Problem). · doi:10.1109/TAC.1971.1099819
[4]Silverman, L. M., Realization of linear dynamical systems, ibid. IEEE Transactions on Automatic Control AC-16, pp. 554-567.
[5]Youla, D. C., L. J. Castriota, & H. J. Carlin, Bounded real scattering matrices and the foundations of linear passive network theory. Trans. IRE Circuit Theory CT-4, 102-124 (1959).
[6]Meixner, J., On the theory of linear passive systems. Arch. Rational Mech. Anal. 17, 278-296 (1964). · Zbl 0173.43205 · doi:10.1007/BF00282291
[7]Willems, J. C., The generation of Lyapunov functions for input-output stable systems. SIAM J. Control 9, 105-134 (1971). · Zbl 0224.93029 · doi:10.1137/0309009
[8]Willems, J. C., Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control AC-16, 621-634, December (1971). (Special issue on the Linear-Quadratic-Gaussian Problem).
[9]Kleinman, D. L., On an iterative technique for Riccati equation computations. IEEE Transactions on Automatic Control AC-13, 114-115 (1968). · doi:10.1109/TAC.1968.1098829
[10]Mårtensson, K., On the matrix Riccati equation. Information Sciences 3, 17-49 (1971). · Zbl 0206.45602 · doi:10.1016/S0020-0255(71)80020-8
[11]Haynsworth, E. V., Determination of the inertia of a partitioned Hermitian matrix. Linear Algebra and Its Applications 1, 73-81 (1968). · Zbl 0155.06304 · doi:10.1016/0024-3795(68)90050-5
[12]Kalman, R. E., Lyapunov functions for the problem of Lur’e in automatic control. Proc. Nat. Acad. Sci. U.S.A. 49, 201-205 (1963). · Zbl 0113.07701 · doi:10.1073/pnas.49.2.201
[13]Yacubovich, V. A., Absolute stability of nonlinear control in critical cases, I and II. Automation and Remote Control 24, 273-282 (1963) and 655-668 (1964).
[14]Popov, V. M., Hyperstability and optimality of automatic systems with several control functions. Rev. Roumaine Sci. Tech. Electrotechn. et Energ. 9, 629-630 (1964).
[15]Kalman, R. E., On a New Characterization of Linear Passive Systems. Proc. of the First Allerton Conference on Circuit and System Theory, Monticello, Ill., pp. 456-470 (1963).
[16]Youla, D. C., & P. Tissi, N-port synthesis via reactance extraction-Part I. 1966 IEEE Internatl. Conv. Rec., Pt. 7, pp. 183-208 (1966).
[17]Vongpanitlerd, S., & B. D. O. Anderson, Scattering matrix synthesis via reactance extraction. IEEE Transactions on Circuit Theory CT-17, 511-517 (1970). · doi:10.1109/TCT.1970.1083180
[18]Anderson, B. D. O., The inverse problem of stationary covariance generation. Journal of Statistical Physics 1, 133-147 (1969). · doi:10.1007/BF01007246
[19]Willems, J. C., Stationary Covariance Generation via the Algebraic Riccati Equation. Fourth UKAC Control Convention, Manchester, England, 1971.
[20]Breuer, S., & E. T. Onat, On recoverable work in linear viscoelasticity. ZAMP 15, 12-21 (1964). · Zbl 0123.40802 · doi:10.1007/BF01602660
[21]Gantmacher, F. R., The Theory of Matrices. New York: Chelsea 1959.
[22]McMillan, B., Introduction to formal realizability theory, I and II. Bell System Tech. J. 31, 217-279 and 541-600 (1952).
[23]Meixner, J., Thermodynamic Theory of Relaxation Phenomena, pp. 73-89 in: Non-Equilibrium Thermodynamics, Variational Techniques and Stability (R. J. Donnelly, R. Herman, & I. Prigogine, Eds.). The University of Chicago Press 1966.
[24]Truesdell, C., Rational Thermodynamics. New York: McGraw-Hill 1969.
[25]Newcomb, R. W., Linear Multiport Synthesis. New York: McGraw-Hill 1966.
[26]Widder, D. V., The Laplace Transform. Princeton University Press 1946.
[27]Weiss, L., & R. E. Kalman, Contributions to linear system theory. Int. J. Engrg. Sci. 3, 141-171 (1965). · Zbl 0136.08702 · doi:10.1016/0020-7225(65)90042-X
[28]Belevitch, V., Classical Network Synthesis. Princeton: Van Nostrand 1968.
[29]Gurtin, M. E., & E. Sternberg, On the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 11, 291-356 (1962). · Zbl 0107.41007 · doi:10.1007/BF00253942
[30]Day, W. A., Time-reversal and the symmetry of the relaxation function of the linear viscoelastic material. Arch. Rational Mech. Anal. 40, 149-159 (1971). · Zbl 0216.51104 · doi:10.1007/BF00281479
[31]Brockett, R. W., & R. A. Skoog, A New Perturbation Theory for the Synthesis of Non-linear Networks, pp. 17-33 of the SIAM-AMS Proceedings on: Mathematical Aspects of Electrical Network Analysis. Am. Math. Soc., 1971.
[32]Gurtin, M. E., & I. Herrera, On dissipation inequalities and linear viscoelasticity. Quart. Appl. Math. 23, 235-245 (1965).