ℋ∞ Consensus for Discrete-time Multi-agent Systems Subject to Distributed Delay and Switching Topologies

• Published in: Chinese Control Conference pp. 2033 - 2038
• Main Authors: Zhang, Bojun, Huang, Hanqiao, Xu, Xinpeng, Cheng, Haoyu, Wei, Yali
• Format: Conference Proceeding
• Language: English
• Published: Technical Committee on Control Theory, Chinese Association of Automation 26.07.2021
• Subjects: Average dwell-time; Consensus; Delays; Dynamic output feedback protocol; Multi-agent system; Protocols; Reduced order systems; Simulation; Stability analysis; Switches; Time-varying delay; Topology
• ISSN: 1934-1768
• DOI: 10.23919/CCC52363.2021.9550733

This paper is concerned with the issue of weighted {\mathcal{H}_\infty } consensus for discrete-time multi-agent systems with time-varying delay and switching topologies. The objective is designing a dynamic output feedback protocol in the presence of external perturbations such that the system achieves consensus in mean square and has a prescribed {\mathcal{H}_\infty } performance level. Firstly, the {\mathcal{H}_\infty } consensus design is converted to a standard {\mathcal{H}_\infty } control problem by reconstructing the closed-loop system as a reduced-order system. Then, by means of the multiple Lyapunov-Krasovskii functional method, the delay-dependent bounded real lemma is derived to guarantee the stability of closed-loop system. Based on these, sufficient conditions for the existence of the required dynamic output feedback protocol is developed in the form of a series of solvable linear matrix inequalities. Finally, numerical example and simulation results are given to illustrate the effectiveness of the obtained results.