Consensus of nonlinear dynamical networks with Markovian switching topologies and time-varying delay

This paper addresses the consensus problem for complex dynamical networks with each node being a Lure system whose nonlinearity satisfies a sector condition. Communication time-delay and Markovian switching topologies are also considered in the dynamical network system. The switching for topologies is determined by a Markov chain, each topology corresponding to a state of the Markov chain. The partial stability theory, Lyapunov-Krasovskii function and Schur complement formula are applied to get the novel criterion, which have the forms of bilinear matrix inequalities. Moreover, the method of designing a static output controller is provided. Finally, numerical examples are presented to illustrate the efficiency and applicability of the proposed methods.