On the State-Space Realization of 2-Periodic Image Behaviors

In this paper we study the realization of periodically time-varying behavioral systems by means of periodic state-space models. In particular, we focus on the case of period two and investigate under which conditions a given behavior with periodic representation obtained by alternating two time-invariant image representations can be realized by a periodic state-space system. We first show that, in general, one cannot expect to obtain a periodic state-space realization by means of the individual realizations of each associated time-invariant behaviors. However, we give conditions for such procedure to hold. The presented results are illustrated by examples.