Elimination of Fixed Modes by Means of High-Performance Constrained Periodic Control

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 and structured decentralized fixed mode are equivalent for this class of systems. If the system is stabilizable under a general decentralized controller (e.g. nonlinear and time-varying), then it is proved that a decentralized LTI discrete-time compensator followed by a zero-order hold can stabilize the system. Moreover, the problem of designing a structurally constrained controller for an interconnected system is converted to the design of a decentralized compensator and a decentralized hold function for an expanded system in order to take advantage of the available methods for decentralized control design. The efficacy of this work is demonstrated in two numerical examples