Model Following with Global Asymptotic Stability in Hybrid Systems with Periodic State Jumps

This work deals with model following by output feedback in hybrid systems subject to periodic state jumps. In particular, the hybrid systems addressed exhibit a free jump dynamics and a to-be-controlled flow dynamics. Moreover, they may present a direct algebraic link from the control input to the regulated output — such possible algebraic link is briefly called the control feedthrough. The problem of structural model following is investigated first. Namely, the structural aspect of model following consists in designing an output feedback hybrid compensator such that the output of the compensated system perfectly replicates that of the reference model for all the admissible input signals and all the admissible sequences of jump times, provided that the compensated system, the reference model, and the feedback compensator have zero initial conditions. A necessary and sufficient condition for the existence of a solution to the structural problem is proven. Then, the problem of also ensuring global asymptotic stability of the closed-loop compensated system, when the state is subject to periodic state jumps, is tackled and a necessary and sufficient condition to accomplish also this goal, under suitable assumptions, is shown.