Consensus of multi-agent systems under a class of randomly time-varying networks

Consensus of multi-agent systems under random networks has attracted considerable attention. In previous literatures, it is often assumed that the agents communicate through Markov switching networks. However, in some engineering applications, the available network information is the expectation of the Laplacian matrix and the time-varying networks are not proper to be regarded as Markov switching. To solve this problem, we develop a method to cope with the mean square consensus of multi-agent systems. Based on the properties of expectation of Laplacian matrix, we present the design of relevant parameters and establish some conditions to guarantee the mean square consensus. Numerical simulations are also given to validate our approach.