Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies

Stochastic consensus problems for linear time-invariant multi-agent systems over Markovian switching networks with time-varying delays and topology uncertainties are dealt with. By using the linear matrix inequality method and the stability theory of Markovian jump linear system, we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the Markov process, provided the union of topologies associated with the positive recurrent states of the Markov process admits a spanning tree and the agent dynamics is stabilizable. Feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying delays. Numerical examples are given to show the feasibility of theoretical results.