Mode-based triggered protocol for synchronization of switched dynamic networks with semi-Markov kernel and its application

In this paper, the mean square synchronization is investigated for discrete-time dynamic networks with stochastic switching topologies via a semi-Markov kernel approach. A novel mode-based triggered protocol is developed to reduce the communication frequency, where the data between coupled nodes is only transmitted at the topology switching instants. Besides, a more general semi-Markov chain based on the semi-Markov kernel approach is first adopted to describe the stochastic switching process of network topologies, then the different types of probability density functions can coexist in any topological mode. Under the proposed triggering strategy, a mode-based distributed synchronization protocol is formed to deal with the controller design difficulty caused by the randomness of semi-Markov switching. Based on the Lyapunov function, some auxiliary inequalities in existing results are avoided and further the numerically testable criterion is obtained to ensure mean square synchronization of the dynamic networks. Finally, a practical example of power systems is presented to demonstrate the effectiveness of the proposed method.