Adaptive cooperative output regulation of discrete-time linear multi-agent systems by a distributed feedback control law

Abstract

An approach based on the discrete-time adaptive distributed observer was recently proposed to solve the cooperative output regulation problem for discrete-time linear multi-agent systems. The validity of this approach relies on the assumptions that the solution to the regulator equations is unique and all the eigenvalues of the leader's system matrix are inside or on the unit circle. In this paper, we will first establish the existence condition of the discrete-time adaptive distributed observer without assuming that the eigenvalues of the leader's system matrix are inside or on the unit circle. Then we will further extend the existing adaptive control approach to the case where the solution to the regulator equations may not be unique. The new results in this paper have enlarged the systems that can be handled by the existing approach. The effectiveness of the proposed approach will be illustrated by an example.