Output-Feedback Model Matching with Strong Stability for Hybrid Linear Systems with Periodic State Jumps

This paper investigates the problem of model matching with strong stability for hybrid linear systems subject to periodic state jumps. The system and the model share the same hybrid time domain: i.e., they exhibit a continuous-time behavior except at certain isolated time instants, where their state shows abrupt discontinuities. The set of the admissible jump time sequences consists of the sequences of equally-spaced time instants whose period is no smaller than a positive real constant. The compensation scheme includes a hybrid dynamic regulator, defined over the same time domain, and a static output-feedback gain. The problem is to determine the hybrid regulator, the feedback gain and the positive time constant in such a way that: (i) the forced response of the closed-loop hybrid system matches that of the hybrid model for all the admissible inputs and for all the admissible jump time sequences; (ii) both the closed-loop hybrid system and the hybrid regulator are globally asymptotically stable for all the admissible jump time sequences. The existence of a solution to the stated problem is characterized by a necessary and sufficient condition.