Exponential stabilization of stochastic  complex networks with Markovian switching topologies via intermittent discrete-time state observations 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 control system is Markovian switching and it is neither required that all switching subnetworks contain a spanning tree nor that they are strongly connected. Moreover, a new type of control, aperiodically intermittent discrete-time state observations control, is proposed. By using the Lyapunov method and graph theory, a theorem with the sufficient conditions for exponential convergence of the state to zero and two corollaries are established. In addition, our theoretical results are used to discuss 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.