Structural properties of linear discrete periodic systems based on fully actuated system approaches

In this paper, the structural properties of linear discrete-periodic systems are investigated using fully actuated system approaches and the related criteria are presented, with emphasis on the observability and controllability criteria based on fully actuated system approaches. Both the high-order fully measured and high-order fully actuated models of linear discrete periodic time-varying systems are constructed, and it is shown that a sufficient and necessary condition for the linear discrete periodic system to be observable (controllable) is that it can be equivalently transformed into a step-forward high-order fully measured (fully actuated) model and a step-backward high-order fully measured (fully actuated) model. Finally, a numerical example is offered to demonstrate the validity and feasibility of the approach.