Stabilization of decentralized control systems by means of periodic feedback

This paper deals with structurally constrained periodic control design for interconnected systems. It is assumed that the system is linear time-invariant (LTI), observable and controllable, and that its modes are distinct and nonzero. It is shown that the notions of quotient fixed mode (QFM) and structured decentralized fixed mode (SDFM) are equivalent for this class of systems. Then, it is proved that if the system is decentrally stabilizable, then one candidate for the decentralized stabilizing controller is a time-varying one consisting of a decentralized LTI discrete-time compensator and a zero-order hold. More specifically, the non-quotient fixed modes of the system will be eliminated via sampling for almost all sampling periods, while any QFM will still remain a fixed mode. The results obtained are ultimately extended to the case when the system has some repeated modes, none of which is a DFM.