Average consensus of a class of multi-agent systems with Markov switching topology and time-varying delays

Considering the network restrictions such as multiple time-varying delays, Markov random switching topology, average-consensus sufficient conditions for the multi-agent network systems with time-delay are proposed. Firstly, by using the idea of state decomposition, consensus problem is converted into analysis system stability. And then, by using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system. Considering multiple time-varying delays and switching topologies, Lyapunov-Krasovskii functional is constructed to analyze the stability. The conservatism of the algorithm is reduced by using free-weighting matrices method. Numerical simulations show the effectiveness of our theoretical results.