Some further results for finite‐time stability of impulsive nonlinear systems

Abstract

This work focuses on Lyapunov‐based finite‐time stability (FTS) theory for impulsive systems. By virtue of a weak Lyapunov inequality condition, which is less restrictive than conditions in most existing results, some further FTS results including settling‐time estimation are derived for impulsive nonlinear systems, under different constraints of impulse time sequences. The impact of impulse jumps on FTS is investigated mathematically from different aspects such as the number and magnitude of impulses, the impulse times, and average impulsive interval (AII) of impulse time sequence. It is found that under relatively weak Lyapunov condition for continuous dynamics, suitable impulses can influence not only the finite‐time convergence (FTC) and settling‐time of a solution, but also the attraction domain of the origin of FTS, which has not been reported in the existing literatures. In particular, stabilizing impulses may change the locality and globality characteristics of FTS. An illustrative example is given to validate the theoretical results.