Reset control systems: stabilization by nearly-periodic reset

In this paper the class of linear impulsive systems is considered. These systems are those with a continuous 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 nearlyperiodic only, i.e. it is distant from a periodic sequence to an uncertain distance. This paper succeeds to state tractable conditions to analyze the stability, and to design reset matrices such that the hybrid system is globally asymptotically stable to the origin. The approach is based on a polytopic embedding of the uncertain dynamics. An example illustrates the main stability result.