Multi-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology

Tong Guo; Jing Han; Cancan Zhou; Jianping Zhou; Tong Guo; Jing Han; Cancan Zhou; Jianping Zhou

doi:10.3934/mbe.2022353

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 7504-7520. doi: 10.3934/mbe.2022353

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Research article

Multi-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology

1.
School of Computer Science & Technology, Anhui University of Technology, Ma'anshan 243032, China
2.
School of Electronical Information Engineering, Wanjiang University of Technology, Ma'anshan 243031, China

Academic Editor: Gail Wolkowicz

Received: 23 March 2022 Revised: 13 May 2022 Accepted: 16 May 2022 Published: 20 May 2022

The multi-leader-follower group consensus issue of a class of stochastic time-delay multi-agent systems subject to Markov switching topology is investigated. The purpose is to determine a distributed control protocol to make sure that the followers' states converge in mean square to a convex hull generated by the leaders' states. Through a model transformation, the problem is transformed into a mean-square stability issue of a new system. Then, an easy-to-check sufficient condition for the solvability of the multi-leader-follower group consensus issue is proposed by utilizing the Lyapunov stability theory, graph theory, as well as several inequality techniques. It is shown that the required feedback gain can be acquired once the condition is satisfied. Finally, an example is used to illustrate the effectiveness of the control protocol.
- multi leaders,
- Markov switching,
- time delay,
- group consensus
Citation: Tong Guo, Jing Han, Cancan Zhou, Jianping Zhou. Multi-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 7504-7520. doi: 10.3934/mbe.2022353

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Abstract

The multi-leader-follower group consensus issue of a class of stochastic time-delay multi-agent systems subject to Markov switching topology is investigated. The purpose is to determine a distributed control protocol to make sure that the followers' states converge in mean square to a convex hull generated by the leaders' states. Through a model transformation, the problem is transformed into a mean-square stability issue of a new system. Then, an easy-to-check sufficient condition for the solvability of the multi-leader-follower group consensus issue is proposed by utilizing the Lyapunov stability theory, graph theory, as well as several inequality techniques. It is shown that the required feedback gain can be acquired once the condition is satisfied. Finally, an example is used to illustrate the effectiveness of the control protocol.

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