Necessary and sufficient conditions for asymptotic model matching of switching linear systems

This paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model, in case both the plant and the model are switching linear systems. Matching has to be achieved, with stability of the feedback loop, for any initial conditions of the plant, the model and the controller (in case it is dynamic) and for any choice of the switching law. Solvability of the problem is characterized in terms of necessary and sufficient conditions that, in part, refer to the geometric structure of the difference system which compares the output of the model and of the plant. Stability is considered both for slow switching and for arbitrary switching. Proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching, respectively, when the state of the model is measurable and when it is not. Weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided, both in the general situation and under slightly restrictive hypotheses.