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

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper studies the finite-time stability problem of nonlinear impulsive time-varying systems and obtains improved Lyapunov theorems and investigates the impulse effects on stability and settling-time. The study introduces parameters to discuss the characteristics of impulses in detail, and proposes a more accurate estimation method for settling-time.