Finite-time stability of solutions for non-instantaneous impulsive systems and application to neural networks

Abstract

This work extends the finite-time stability (FTS) results to non-instantaneous impulsive time-varying systems on the basis of general impulsive systems via Lyapunov theory. The impacts of impulse numbers, impulse time sequences and impulse amplitudes on FTS and settling-time estimation are discussed. The effects of different types of impulses on settling-time are discussed when the impulse number is known or pre-given. The average impulsive interval is introduced to extend the above results to the case when the impulse number is unknown, and the derivative of Lyapunov function is allowed to be indefinite instead of being negative definite or semi-negative definite. Moreover, the theoretical results are applied to non-instantaneous impulsive neural networks. Finally, we provide two numerical examples to demonstrate the effectiveness and feasibility of the obtained results.