Bulletin of the American Mathematical Society

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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.

T. A. Burton, Uniform asymptotic stability in functional differential equations, Proc. Amer. Math. Soc. 68 (1978), no. 2, 195–199. MR 481371, DOI 10.1090/S0002-9939-1978-0481371-5

J. R. Haddock and J. Terjéki, Liapunov-Razumikhin functions and an invariance principle for functional-differential equations, J. Differential Equations 48 (1983), no. 1, 95–122. MR 692846, DOI 10.1016/0022-0396(83)90061-X

Wolfgang Hahn, Theory and application of Liapunov’s direct method, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. English edition prepared by Siegfried H. Lehnigk; translation by Hans H. Losenthien and Siegfried H. Lehnigk. MR 0147716

Jack K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39–59. MR 244582, DOI 10.1016/0022-247X(69)90175-9

Jack Hale, Theory of functional differential equations, 2nd ed., Applied Mathematical Sciences, Vol. 3, Springer-Verlag, New York-Heidelberg, 1977. MR 0508721

Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244

[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.

J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968), 57–65. MR 222402, DOI 10.1016/0022-0396(68)90048-X

[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)

G. Makay, On the asymptotic stability in terms of two measures for functional-differential equations, Nonlinear Anal. 16 (1991), no. 7-8, 721–727. MR 1097328, DOI 10.1016/0362-546X(91)90178-4

[13]

M. Marachkov, On a theorem on stability, Bull. Soc. Phys. Math. 12 (1940), 171-174.

Taro Yoshizawa, Asymptotic behavior of solutions of a system of differential equations, Contributions to Differential Equations 1 (1963), 371–387. MR 148991

[15]

-, Stability theory by Liapunov's second method, Math. Soc. Japan Tokyo, 1966.

[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.