Electron. J. Diff. Eqns., Vol. 2001(2001), No. 34, pp. 1-13.

Exponential stability of nonlinear time-varying differential equations and applications

N. M. Linh & V. N. Phat

Abstract:
In this paper, we give sufficient conditions for the exponential stability of a class of nonlinear time-varying differential equations. We use the Lyapunov method with functions that are not necessarily differentiable; hence we extend previous results. We also provide an application to exponential stability for nonlinear time-varying control systems.

Submitted September 20, 2000. Published May 14, 2001.
Math Subject Classifications: 34K20, 34D10, 49M37.
Key Words: Exponential stability, time-varying equations, Lyapunov function, Lipschitz condition, control systems.

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Nguyen Manh Linh
Institute of Mathematics
National Center for Sciences and Technology
P.O. Box 631 Bo Ho, 10.000 Hanoi, Vietnam
Vu Ngoc Phat
Institute of Mathematics
National Center for Sciences and Technology
P.O. Box 631 Bo Ho, 10.000 Hanoi, Vietnam
e-mail: vnphat@hanimath.ac.vn
e-mail: phvu@syscon.ee.unsw.edu.au

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