Book Review

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Book Information:

Author: V. M. Matrosov V. Lakshmikantham, 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.

**[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.

Review Information:

Reviewer: T. A. Burton

Journal: Bull. Amer. Math. Soc.

**26**(1992), 344-348

DOI: https://doi.org/10.1090/S0273-0979-1992-00275-6