Stabilization of linear impulsive systems through a nearly-periodic reset

Abstract

This paper deals with the class of impulsive systems constituted by a continuous-time linear dynamics for all time, except at a sequence of instants. When such a discrete time occurs, the state undergoes a jump, or more precisely follows a discrete linear dynamics. The sequence of time instants, when a discrete dynamics occurs, is nearly-periodic only, i.e. it is distant from a periodic sequence to an uncertain error. This paper succeeds to state tractable conditions to analyze the stability, and to design reset matrices such that the hybrid system is globally exponentially stable to the origin. The approach is based on a polytopic embedding of the uncertain dynamics. Some examples illustrate the main results.