Dynamic event-triggered H∞ leader-following consensus for nonlinear stochastic multi-agent systems with semi-Markov switching topologies and application

This paper investigates the $H_{\infty }$ leader–follower mean-square consensus problem for nonlinear stochastic multi-agent systems with semi-Markov switching topologies. We address the scenario where the partial communication topology has a directed spanning tree, thus eliminating the special condition that each communication topology must have a directed spanning tree. Given the finite system resources, to minimize unnecessary waste, an improved dynamic event-triggered protocol is designed. To tackle the modal mismatch between the system and the controller, an asynchronous controller with non-homogeneous hidden semi-Markov chains is introduced. Subsequently, by constructing a suitable Lyapunov function, we derive sufficient conditions for the system to achieve leader–follower $H_{\infty }$ mean-square consensus and meet the performance index $\gamma$. Thereafter, the obtained results are applied to address the $H_{\infty }$ leader–follower mean-square consensus of stochastic multi-agent systems under network attacks. Finally, numerical simulations are employed to validate the effectiveness of the theoretical results.