Containment Control of Multi-Agent Systems over Directed Graphs: A Delay Robustness Perspective

This paper investigates the delay range optimization for robust containment control of first-order multi-agent systems over directed graphs. The purpose is to find the maximum allowable delay range within which the multi-agent system can achieve containment robustly under P and PD containment control protocols subject to communication delay. This means that a group of follower agents converge to the convex hull formed by the multiple leader agents under a distributed control protocol. In this paper we focus on a continuous first-order multi-agent system in which each individual agent has an unstable real pole. The connected graph among agents is directed graph, and followers can receive information from leaders as well as from other followers, in which each leader has at least one global accessible path for all followers, and leaders do not communicate with each other. By using the frequency domain analysis method, we provide the exact expression and the bounds on the maximum allowable delay range for robust containment control of multi-agent systems. The results show that the position of the pole and the network connectivity will affect the delay bound. Finally, numerical examples are given to illustrate the effectiveness of our proposed results. Copyright (C) 2021 The Authors.