Set theory conditions for stability of linear impulsive systems

Abstract

In this paper we give tractable necessary and sufficient condition for the global exponential stability of a linear impulsive system. The reset rule considered in the paper is quasi-periodic and the stability analysis is based on a standard tool in set theory that is Minkowski functional. Firstly, we reformulate the problem in term of discrete-time parametric uncertain system with the state matrix belonging to a compact but non-convex set. Secondly, we provide a tractable algorithm for testing the stability and computing the associated polyhedral Lyapunov function when the system is stable. The main result is an algorithm whose computational effort is analogous to that of classical algorithms for contractive polytopes computation for discrete-time parametric uncertain systems with the state matrix belonging to a polytopic set.