Finite‐time stability for time‐varying nonlinear impulsive systems

Abstract

This paper investigates the finite‐time stability (FTS) for time‐varying nonlinear impulsive systems. We provide several Lyapunov‐based theorems to ensure the FTS property, where three types of impulses including stabilizing impulses, destabilizing impulses, and multiple impulses are fully considered. The relation of the settling‐time and the impulse sequences is established. It shows that the settling‐time of the system can be shortened for the stabilizing impulses and be postponed for the destabilizing ones. In particular, under the effect of multiple impulses, the settling‐time estimation is derived via a sequence division method. Moreover, we apply the theoretical results to the control problem of coupled impulsive neural networks (CINNs) involving time‐varying uncertainties, where the control scheme is designed to guarantee the FTS of the considered systems. The effectiveness of presented results is illustrated by three simulation examples.