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

In this paper, the $ H_{\infty } $ H∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $ (x, u, v) $ (x,u,v)-dependent noises is studied. Firstly, the $ H_{\infty } $ H∞ consensus problem is transformed into a standard $ H_{\infty } $ H∞ 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 } $ H∞ 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 {\rm {o}} $ o^ formula. Finally, we illustrate the validity of the developed method with numerical simulations.