Stability and stabilization of discrete-time linear systems with nearly-periodic impulses

This paper deals with stability analysis and controller design problems for discrete-time linear systems with nearly-periodic impulses. The interval of such impulses consists of a nominal value and an uncertain time-varying bounded term. That is, the error between impulsive sequences and a periodic sequence is an uncertain bounded value. Using linear difference inclusion methods and convex combination techniques, a time-varying Lyapunov function which contains the information of impulsive intervals is introduced for stability anlysis and a novel uniform global exponential stability criterion is derived in terms of linear matrix inequalities. Sufficient conditions for the existence of reduced-order and full-order impulsive controllers which can utilize the system output information are presented. Finally, three examples are provided to demonstrate the effectiveness of the developed results.