Robust Stability for Impulsive Systems With Polytope Uncertainties

This paper is concerned with robust stability for impulsive systems with polytope uncertainties. At first, the stability for impulsive systems without uncertainties is addressed by employing a Lyapunov-like functional. The Lyapunov-like functional is time-varying, discontinuous, and not imposed to be definite positive. Compared with the existing Lyapunov functional built on [t(k), t], a part of the impulsive interval [t(k), t(k+1)], the Lyapunov-like functional is two-sided in terms of employing the system information on [t, t(k+1)] as well as [t(k), t]. When estimating the derivative of the time-varying and two-sided Lyapunov-like functional, which includes integrals of the state and integrals coupled by [t, t(k+1)] and [t(k), t], integral equations of the impulsive system are introduced and an advanced inequality is employed. By the Lyapunov-like functional theory, a new stability result is obtained for impulsive systems without uncertainties. Then, the stability result is adapted to impulsive systems with polytopic uncertainties and a robust stability result is derived. At last, the numerical examples are given to illustrate that the stability results for impulse systems with or without polytopic uncertainties improve over some existing ones.