Observer-based mean square consensus of nonlinear networked systems under Markov switching communication topologies

This paper aims to investigate the mean square consensus (MSC) problem of a class of nonlinear networked systems subject to directed and stochastic switching communication topologies, where the switching law is determined by an ergodic continuous-time Markov process. The cooperative consensus controller is designed by using an observer-based method. Firstly, for the case with Lur'e nonlinear dynamics, by developing a stochastic Lyapunov function, we show that the MSC under consideration can be realized if the union of the underlying network graphs has a directed spanning tree. It is worth noting that none of the network graphs is required to contain a directed spanning tree. Moreover, we study the MSC problem for networked systems with Lipschitz-type nonlinear dynamics. Finally, a numerical simulation is conducted on multiple Chua's circuit systems to illustrate the effectiveness of the proposed controllers.