This paper investigates the mean square consensus problem for continuous-time multiagent systems with randomly switching topologies and noises. The switching is governed by a time-homogeneous Markov process, and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of the Markov process. Then, necessary and sufficient conditions can be obtained under a control protocol with time-varying gain. Moreover, we extend our result to the cases where the topological structure is semi-Markovian switching and the elements of transition rate matrix are partly unknown. Finally, we give an example to illustrate the validity of our results.

This article addresses the practical output consensus of a class of heterogeneous leader–follower multiagent systems with directed network topology. The total disturbance of each agent, which is the nonlinear coupling effect of disturbances, uncertainties, and measurement noises mismatched with control inputs in large scale, is estimated in real time by a set of extended state observers. Extended state observers-based consensus protocols are then designed to obtain the output consensus, with the total disturbance of each agent be rejected actively. Both the convergence of the tracking error between outputs of all followers and the output of the leader in practical sense and the boundedness of all states are presented with theoretical analysis. Finally, the rationality of the control strategy and main result are verified by a numerical example.