Further results on periodically time-varying behavioral systems

We consider periodic behavioral systems as introduced in [1] and analyze two main issues: behavior representation and controllability. More concretely we study the equivalence and the minimality of representations. Moreover we relate the controllability of a periodic system with the controllability of an associated time-invariant system known as lifted system, and derive a controllability test. Finally we prove the existence of an autonomous/controllable decomposition similar to what happens for the time-invariant case.