\(H_\infty\) consensus of stochastic multi-agent systems with time-delay and Markov jump. (English) Zbl 07885498
Summary: In this paper, the \(H_\infty\) consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and \((x, u, v)\)-dependent noises is studied. Firstly, the \(H_\infty\) consensus problem is transformed into a standard \(H_\infty\) 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 \(H_\infty\) 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 Itô formula. Finally, we illustrate the validity of the developed method with numerical simulations.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93D50 | Consensus |
| 93E03 | Stochastic systems in control theory (general) |
| 93C10 | Nonlinear systems in control theory |
| 93A16 | Multi-agent systems |
| 93B52 | Feedback control |
| 93C43 | Delay control/observation systems |
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