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 multi-agent 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 multi-pendulum systems demonstrates their effectiveness.