H_∞ consensus of multi-agent systems with semi-Markovian switching topologies and mode-dependent delays

Abstract

This paper addresses $H_{\mathrm{\infty }}$ leader-following consensus of multi-agent systems with semi-Markovian switching topologies and time-varying delays. Unlike the classic Markovian switching topologies, the transition rates are time-varying in the semi-Markovian switching topologies, which can better model the switching of topologies due to inevitable stochastic changes. Moreover, compared with existing works on multi-agent systems with switching topologies and time delays, the delays in the paper are dependent on the switching modes. By designing the distributed mode-dependent consensus protocol and constructing Lyapunov functional, sufficient conditions in terms of LMIs are derived to ensure that $H_{\mathrm{\infty }}$ leader-following consensus is asymptotically achieved in the mean square. Finally, a numerical example is provided to show the effectiveness of the main results.

Keywords:

• Multi-agent systems
• semi-Markovian switching topologies
• mode-dependent delays
• $H_{\mathrm{\infty }}$ consensus

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

National Natural Science Foundation of China [grant number 11971444].

Notes on contributors

Xiaowu Mu

Xiaowu Mu received his B.S., M.S. and Ph.D. degrees from the Department of Mathematics of Peking University in 1983, 1988 and 1991, respectively. Currently, he is a Professor in Zhengzhou University. His research interests include stochastic systems, hybrid systems, nonlinear control, and networked control systems.

Minhong He

Minhong He received his B.S., M.S. and Ph.D. degrees from the School of Mathematics and Statistics of Zhengzhou University in 2008, 2011 and 2020, respectively. Currently, he works at Hefei University. His research interests include multi-agent systems, networked control systems and stochastic systems.