Novel dwell-time dependent stability results for impulsive systems

Abstract

This paper investigates the dwell-time stability for impulsive systems by employing a Lyapunov-like functional that is time-varying, discontinuous, and not imposed to be definite positive. Employing the system information on the impulsive interval wholly rather than partly, a concrete Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the impulsive state. To take advantage of the integral of the system state, integral equations of the impulsive system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, new dwell-time dependent stability results with ranged dwell-time, maximal dwell-time and minimal dwell-time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which is illustrated by numerical examples.