Cooperative Output Regulation of Discrete-Time Linear Time-Delay Multi-agent Systems

TL;DR

This paper addresses the cooperative output regulation problem for discrete-time linear multi-agent systems with time delays, introducing new challenges and solutions distinct from continuous-time systems.

Contribution

It develops a novel distributed observer approach for discrete-time systems and solves the regulation problem using dynamic output feedback control.

Findings

Existence conditions for discrete distributed observers are established.

A distributed dynamic output feedback control law is proposed.

The approach extends cooperative control to discrete-time systems with delays.

Abstract

In this paper, we study the cooperative output regulation problem for the discrete linear time-delay multi-agent systems by distributed observer approach. In contrast with the same problem for continuous-time linear time-delay multi-agent systems, the problem has two new features. First, in the presence of time-delay, the regulator equations for discrete-time linear systems are different from those for continuous-time linear systems. Second, under the standard assumption on the connectivity of the communication graph, a distributed observer for any continuous-time linear leader system always exists. However, this is not the case for discrete-time systems, and the behavior of a distributed observer is much more complicated. Thus, we will first study the existence of the discrete distributed observer, and then present the solvability of the problem by distributed dynamic output feedback control law.