consensus of stochastic multi-agent systems with time-delay and Markov jump

Abstract

In this paper, the $H_{\mathrm{\infty }}$ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $(x,u,v)$-dependent noises is studied. Firstly, the $H_{\mathrm{\infty }}$ consensus problem is transformed into a standard $H_{\mathrm{\infty }}$ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified $H_{\mathrm{\infty }}$ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It$\hat{\mathrm{o}}$ formula. Finally, we illustrate the validity of the developed method with numerical simulations.

Keywords:

• Multi-agent systems
• output feedback control
• time-delay
• Markov jump

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62373205 and 62033007), Taishan Scholars Project of Shandong Province of China (No. tstp20230624, ts20190930) and Taishan Scholars Climbing Program of Shandong Province of China.