Exponential stabilization of stochastic complex networks with Markovian switching topologies via intermittent discrete-time state observation control

Abstract

This paper is concerned with the exponential stability of the stochastic complex networks with Markovian switching topologies. It is worth emphasizing that the topological structure of the stochastic complex networks is Markovian switching. Not all switching subnetworks must contain a spanning tree or be strongly connected. Moreover, a new type of aperiodically intermittent discrete-time state observation control is proposed, which is a significant extension of discrete-time state observation control and intermittent control. Based on the M-matrix, the Lyapunov method, and the graph theory, some sufficient conditions for exponential convergence. Moreover, we obtain that the average control rate in this paper is greater than the control rate proposed in the existing literature, which is less conservative. In addition, the theoretical results are used to discuss the exponential stability of stochastic coupled oscillators and a communication network model, respectively. Finally, two numerical examples are given to verify the effectiveness of the results.