Structural model matching in hybrid linear systems with state jumps

This work deals with structural model matching by output feedback in hybrid linear systems subject to state jumps. Namely, given a hybrid linear plant and a hybrid linear model, the problem consists in finding a hybrid linear regulator that achieves exact matching between the forced response of the given hybrid linear plant and that of the hybrid linear model, for all the admissible input functions and all the admissible sequences of jump times, by means of a hybrid dynamic feedback of the plant output. In particular, the jump times may not be uniformly spaced in time, with the only constraint that the number of jump times is finite in any finite time interval. A necessary and sufficient condition for the stated problem to have a solution is shown. A complete computational procedure for the synthesis of the regulator is illustrated through the proof of sufficiency, which is constructive.