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Book Review
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Book Information
Author(s):
V. Lakshmikantham, V. M. Matrosov, and S. Sivasundaram
Title:
Vector Lyapunov functions and stability analysis of nonlinear systems
Additional book information:
Kluwer Academic Publishers, Dordrecht, 1991, 172 pp., US$79.00. ISBN 0-7923-1152-3
References:
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- [1]
- T. A. Burton, Uniform asymptotic stability in functional differential equations, Proc. Amer. Math. Soc. 68 (1978), 195-199. MR 0481371 (58:1489)
- [2]
- J. R. Haddock and J. Terjéki, Lyapunov-Razumikhin functions and an invariance principle for functional differential equations, J. Differential Equations 48 (1983), 93-122. MR 692846 (84f:34104)
- [3]
- W. Hahn, Theory and application of Lyapunov's direct method, Prentice-Hall, Englewood Cliffs, NJ, 1963. MR 0147716 (26:5230)
- [4]
- J. K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39-59. MR 0244582 (39:5896)
- [5]
- -, Theory of functional differential equations, Springer, NY, 1977. MR 0508721 (58:22904)
- [6]
- D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer, NY, 1981. MR 610244 (83j:35084)
- [7]
- N. N. Krasovskiĭ, Stability of motion, Stanford, Univ. Press, Stanford, CA, 1963.
- [8]
- V. Lakshmikantham and S. Leela, Differential and integral inequalities, vols. I, and II, Academic Press, NY, 1969.
- [9]
- J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968), 57-65. MR 0222402 (36:5454)
- [10]
- A. M. Liapounoff, Problème générale de la stabilité du mouvement, Ann. of Math. Stud., no. 17, Princeton Univ. Press, Princeton, NJ, 1947. (This is a reprint of the 1907 French Translation.)
- [11]
- A. M. Lyapunov, General problem of stability of motion, Grostechnizdat, Moscow and Leningrad, 1935. (Russian)
- [12]
- G. Makay, On the asymptotic stability in terms of two measures for functional differential equations, Nonlinear Anal. 16 (1991), 721-727. MR 1097328 (92b:34093)
- [13]
- M. Marachkov, On a theorem on stability, Bull. Soc. Phys. Math. 12 (1940), 171-174.
- [14]
- T. Yoshizawa, Asymptotic behavior of solutions of a system of differential equations, Contrib. Differential Equations 1 (1963), 371-387. MR 0148991 (26:6487)
- [15]
- -, Stability theory by Liapunov's second method, Math. Soc. Japan Tokyo, 1966.
Additional Information:
Reviewer(s):
T. A.
Burton
Review Information:
Journal:
Bull. Amer. Math. Soc.
26
(1992),
344-348.
DOI:
10.1090/S0273-0979-1992-00275-6
PII:
S 0273-0979(1992)00275-6
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