Second-Order Locally Dynamical Consensus of Multiagent Systems With Arbitrarily Fast Switching Directed Topologies

This paper is mainly concerned with the analysis of the second-order locally dynamical consensus of multiagent systems with nonlinear dynamics in the directed networks with arbitrarily fast switching topologies. In our designed framework, the time-varying network topology is constant in each time interval and then randomly jumps to another topology when certain occasional events occur at some random moments. In addition, we further assume that the dwell time of each topology is unknown in advance and the corresponding adjacency weighted matrix is not necessarily nonnegative due to the probable existence of deteriorated communication channels in the underlying interaction network. By the orthogonal decomposition method, the state vector of the resultant error dynamical system can be further decomposed as two transversal components, one of which evolves along the consensus manifold and the other evolves transversally with the consensus manifold. Then, by introducing the generalized matrix measure and by applying the tools of contraction and circle analysis, the second-order locally dynamical consensus of multiagent systems with arbitrarily fast switching directed topologies is theoretically investigated in detail, and some easily verified sufficient conditions are also presented. It is shown that, under sufficiently large coupling strengths, the random switchings can be effectively tolerated and the consensus can be achieved for all agents in the network. Finally, numerical simulation examples are also provided to demonstrate the feasibility and effectiveness of the obtained theoretical results.