Controllability and reconstructibility of periodic state space systems – a behavioral approach *

In this paper we view a classical periodic state space system as a behavioral system and compare the properties of state controllability and state reconstructibility with behavioral controllability and behavioral reconstructibility, respectively. We show that, like it happens for the time-invariant case, the behavioral controllability/reconstructibility of a periodic state space system is equivalent to its complete state controllablity/reconstructibility. Further, using the classical definition of a dual state space system and our behavioral definitions, we prove that behavioral controllability and behavioral reconstructibility are also dual properties in the periodic case.