Controllability, autonomicity and free variables in periodic behaviors

In this paper we propose a new type of “image” representation for periodic behaviors and analyze the relationship between image representability and controllability, showing that the correspondence, which exists in the time-invariant case, generalizes to periodic behaviors. We also show that the concept of free variable used in the time-invariant case cannot be transposed to the periodic case in a straightforward manner and introduce a new concept of variable freeness (P-periodic freeness) . This allows us to define input/output structures for periodic behaviors.