Adaptive distributed observer for general linear leader systems over periodic switching digraphs

Abstract

A standard assumption on the existence of the distributed observer or adaptive 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 present sufficient conditions for the existence of both the distributed observer and the adaptive distributed observer for general linear leader systems over periodic jointly connected switching networks. As an application of the distributed observer, we solve the cooperative output regulation problem 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.