Model matching problems for switching linear systems

This paper investigates the problem of designing a feedback compensator to force the response of a plant modeled by a switching linear system to match that of a prescribed, switching linear model, for any choice of the switching law. The problem is stated by considering both the situation in which the state of the model is measurable and that in which it is not. Accordingly, static compensators or, alternatively, dynamic ones will be sought. The additional requirement of asymptotic stability of the compensated system is introduced by reasonably restricting the class of admissible switching laws. Using geometric methods, that extend classic ones to the framework of switching systems, a complete solution, in terms of necessary and sufficient conditions that are algorithmically checkable, is given for matching without stability and for matching with asymptotic stability for a mildly restricted class of plants.