Synchronization of Markovian complex networks with input mode delay and Markovian directed communication via distributed dynamic event-triggered control

Abstract In this study, distributed dynamic event-triggered controller containing Markov switching topologies is proposed in Markovian Complex Networks (MCNs). It is proved that the Zeno-behavior is avoided. Considering that the time delay and the controller vary with different modes in practical applications, two terms of the controller are designed to contain Markov switching. And mode-dependent Lyapunov–Krasovskii functions (LKFs) are constructed, whereby the time-varying delay with Markov switching in the controller is perfectly processed. And by constructing a pair of LKFs, some summation terms containing the transition probability are eliminated. In addition, two synchronization criteria for MCNs with input mode delay and Markovian directed communication are established. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method.