Abstract
We establish new conditions of integral stability and uniform Lipschitz stability based on the use of the comparison principle and a matrix-valued Lyapunov function.
Similar content being viewed by others
References
A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Gostekhizdat, Moscow-Leningrad (1935).
I. Vrkoĉ, “Integral stability”, Czech. Math. J., 84, No. 9, 71–128 (1959).
F. M. Dannan and S. Elaydi, “Lipschitz stability of nonlinear system of differential equations,” J. Math. Anal. Appl., 113, 562–577 (1986).
M. Kudo, “On the integral stability and the uniform integral stability of nonlinear differential equations by using comparison principle,” Res. Repts Akita Nat. College Techn., 23, 67–72 (1987).
V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York (1989).
Lj. Grujic, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale System Stability under Structural and Singular Perturbation, Springer, Berlin (1984).
M. Kudo, “On the uniform Lipschitz stability of nonlinear differential equations by the comparison principle”, Res. Repts Akita Nat. College Techn., 26, 41–43 (1990).
Additional information
Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 49, No. 1, pp. 77–83, January, 1997.
Rights and permissions
About this article
Cite this article
Martynyuk, A.A. On integral stability and Lipschitz stability of motion. Ukr Math J 49, 84–92 (1997). https://doi.org/10.1007/BF02486618
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02486618