A new Lyapunov-like functional approach to dwell-time dependent stability for impulsive systems

Abstract

This paper investigates the dwell-time dependent stability for impulsive systems by employing a new Lyapunov-like functional that is of the second order in time t. In contrary to those built on [tk, t], a part of the impulsive interval [tk,tk+1], the Lyapunov-like functional is two-sided in the sense of employing the system information on [t,tk+1] as well as [tk, t]. To deal with the derivative of the two-sided Lyapunov-like functional, which involves integrals of the state and integrals coupled by [t,tk+1] and [tk, t], integral equations of the impulsive systems are introduced and an advanced inequality is employed. 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 turn out to be less conservative than some existing ones, which is illustrated by numerical examples.