Mean-Square Consensus Seeking over Multi-Interconnection Dynamical Networks with Markovian Switching Topologies

This paper considers the mean-square consensus problem for a nonlinear complex dynamical network system with Markovian switching topologies, topology uncertainties and time-varying delays. For the system, each node is a Lure system whose nonlinearity satisfies a sector condition, and more than one interconnections are considered in view of the fact that the subsystems of networks may be multiple interconnected. By using the linear matrix inequality method and the partial stability theory, sufficient conditions of the exponentially mean-square consensus are obtained for the nonlinear complex dynamical network Lure system in the Markovian switching topologies. Moreover, a novel static output controller has been designed to make the system achieve exponentially mean-square consensus successfully. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.