Abstract
In this paper, structural decomposition of linear periodic continuous-time systems is discussed. It was conjectured by Bittanti and Bolzeron that there exists a periodically time-varying coordinate transformation with the same period of a given linear periodic continuous-time system that splits the system into its controllable and uncontrollable parts. However we have shown that there is a counterexample to this conjecture. In this paper, we firstly study basic properties of controllable/reachable subspaces for linear periodic continuous-time systems. Then we derive a necessary and sufficient condition for the existence of a periodically time-varying coordinate transformation with the same period of the system that splits the system into its controllable and uncontrollable parts.
