Event-triggered consensus control for multi-agent systems with Markov switching topologies

This paper investigates the event-triggered consensus control problem for multi-agent systems with Markov switching topologies. By a linear transformation method, the mean-square consensus problem under event-triggered protocol is transformed into the mean-square stability problem subject to a certain constraint condition. Then by constructing Lyapunov function and employing the weak infinitesimal operator, the mode-dependent consensus controller gains are designed in terms of a bilinear matrix inequality. In order to write bilinear matrix inequality as a set of linear matrix inequalities, three kinds of iterative algorithms are developed. Finally, a simulation example is provided to verify the validity of the presented algorithms.