# Cooperative Robust Output Regulation Problem for Discrete-Time Linear Time-Delay Multi-Agent Systems

## TL;DR

This paper addresses the cooperative robust output regulation problem in discrete-time multi-agent systems with delays, proposing a distributed internal model approach to achieve synchronization despite communication and input delays.

## Contribution

It introduces a novel distributed internal model for delayed multi-agent systems and provides a solution framework under standard assumptions for robust output regulation.

## Key findings

- Successful formulation of the distributed internal model for delayed systems
- Proved that control laws solving auxiliary systems also solve original systems
- Applicable to both state feedback and output feedback control schemes

## Abstract

In this paper, we study the cooperative robust output regulation problem for discrete-time linear multi-agent systems with both communication and input delays by distributed internal model approach. We first introduce the distributed internal model for discrete-time multi-agent systems with both communication and input delays. Then, we define so-called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi-agent systems.