Distributed Observer for General Linear Leader Systems over Periodic Switching Digraphs

A long-standing assumption on the existence of the distributed observer for a linear leader system over jointly connected switching networks is that none of the eigenvalues of the system matrix of the leader system have positive real parts. In this paper, after establishing a stability result for a class of linear periodic switched systems, we show that a distributed observer for general linear leader systems over jointly connected switching networks exists provided that the switching signal is periodic with its period sufficiently small. As an application of the distributed observer, we solve the cooperative output regulation for linear multi-agent systems with general linear leader systems over periodic jointly connected switching networks. A numerical example is provided to illustrate our design.