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

In this paper, the $ H_{\infty } $ H infinity 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 infinity consensus problem is transformed into a standard $ H_{\infty } $ H infinity 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 infinity 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.