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A computational method for determining quadratic Lyapunov functions for non-linear systems. (English) Zbl 0225.34027

34D08Characteristic and Lyapunov exponents
34A34Nonlinear ODE and systems, general
65J99Numerical analysis in abstract spaces
34D20Stability of ODE
Full Text: DOI
[1] Lyapunov, A. M.: Problem general de la stabilite du mouvement (Annuals of mathematics studies). (1949)
[2] Kalman, R. E.; Bertram, J. E.: Control system design via the second method of Lyapunov. Trans. ASME, J. Bas. engng series D 82, 371-393 (1960)
[3] Margolis, S.; Vogt, W.: Control engineering applications of V. I. zubov’s construction procedure for Lyapunov functions. IEEE trans. Aut. control 8, 104-113 (1963)
[4] Zubov, V. I.: Problems in the theory of the second method of Lyapunov construction of the general solution in the domain of asymptotic stability. Prikl. mat. Mekh. 19, 179-210 (1955)
[5] Weissenberger, S.: Stability boundary approximations for relay-control systems via a steepest-ascent construction of Lyapunov functions. Jacc 1965, 584-594 (1965)
[6] Rodden, J. J.: Numerical applications of Lyapunov stability theory. Jacc 1964, 261-268 (1964)
[7] Geiss, G. R.: Estimation of the domain of attraction. Grumman research department (March 1966)
[8] Geiss, G. R.; Cohen, V.; Rothschild, D.: Development of an algorithm for the non-linear stability analysis of the orbiting astronomical observatory control system. Grumman research department (November 1967)
[9] Davison, E. J.; Cowan, K.: A computational method for determining the stability region of a second-order non-linear autonomous system. Int. J. Control 9, 349-357 (1969) · Zbl 0174.47501
[10] Berger, A.; Lapidus, L.: Stability of high dimensional non-linear systems using Krasovskiĭ’s theorem. A.i.ch..e. journal 15, 171-177 (1969)
[11] Lasalle, J.; Lefschetz, S.: Stability by Lyapunov’s direct method with applications. 58-59 (1961)
[12] Rosenbrock, H. H.: An automatic method of finding the greatest or least value of a function. Computer J. 3, 175-184 (1960)
[13] Davison, E. J.; Man, F. T.: The numerical calculation of A’Q + AO = C”. IEEE trans. Aut. control 13, 448-449 (1968)
[14] Greenstadt, J.: The determination of the characteristic roots of a matrix by the Jacobi method. Mathematical methods for digital computers (1964)
[15] Hahn, W.: Theory and application of Lyapunov’s direct method. (1963) · Zbl 0119.07403
[16] Ingwerson, D.: A modified Lyapunov method for non-linear stability analysis. IRE trans. 6, 199-210 (1961)
[17] Ku, H.; Chen, C.: Stability study of a third-order servomechanism with multiplicative feedback control. AIEE trans. 77, 131-136 (1958)