Cooperative Output Regulation for Continuous-Time Linear Periodic Systems

This note investigates the cooperative output regulation problem for linear periodically time-varying systems. The problem is divided into two subproblems: solving periodic differential Sylvester equations (PDSEs) and designing a suitable time-varying distributed controller to stabilize an augmented multiagent system. First, the solvability of the PDSEs is discussed under an observability condition. Then, a dynamic output-feedback controller based on the internal model principle is proposed, which stabilizes the augmented system with local information used. This distributed controller ensures that the closed-loop system states converge to invariant manifolds where the corresponding error map is identically equal to zero. An application of the proposed control laws to linear periodic multipendulum systems demonstrates their effectiveness.