Uniform finite-time stability of nonlinear impulsive time-varying systems

Abstract

Finite-time stability (FTS) problem of nonlinear impulsive time-varying systems is studied in this paper. Some improved Lyapunov theorems on uniform FTS including settling-time estimation are obtained based on a time-varying differential inequality, in which the derivative of Lyapunov function is not necessarily negative definite. Especially, the stabilizing and destabilizing impulse effects on FTS and settling-time are investigated by developing a unified technique, such that the magnitude of impulses, the number of impulses and specific distribution of impulse times may be discussed in detail by introducing proper parameters. Furthermore, more accurate estimation of settling-time can be derived by using these parameters. Finally, two numerical examples are provided to validate the obtained results.