Considering the limited communications conditions such as delays, disturbances, and topologies uncertainties, the stability criteria for robust consensus of multiagent systems are proposed in this paper. Firstly, by using the idea of state decomposition and space transformation, the condition for guaranteeing consensus is converted into verifying the robust stability of the disagreement system. In order to deal with multiple time-varying delays and switching topologies, jointly quadratic common Lyapunov-Krasovskii (JQCLK) functional is built to analyze the robust stability. Then, the numerical criterion can be obtained through solving the corresponding feasible nonlinear matrix inequality (NLMI); at last, nonlinear minimization is used like solving cone complementarity problem. Therefore, the linear matrix inequality (LMI) criterion is obtained, which can be solved by mathematical toolbox conveniently. In order to relax the conservativeness, free-weighting matrices (FWM) method is employed. Further, the conclusion is extended to the case of strongly connected topologies. Numerical examples and simulation results are given to demonstrate the effectiveness and the benefit on reducing conservativeness of the proposed criteria. 1. Introduction Recently, the consensus problem has become an interesting and important topic in the field of formation control, flocking, rendezvous in multiagent systems, fusion estimation, collaborative decision making, and coupled oscillator synchronization. In some practical applications, communication delays and switching topologies should be considered because of agents moving, communication congestion, or finite transmission distance. The earliest work focused on the conditions for guaranteeing that the agents achieve average consensus with time-delays and switching topologies, for example, frequency domain [1–3], time domain [4–8], delay graph [9, 10], and max-min value [11, 12]. These existing methodologies contributed to the average consensus problem with limited networks enormously. Furthermore, there is also some work focusing on the networks with disturbances, and topologies uncertainties, namely, robust consensus. The stability with noises in the multiagent systems has been discussed in [13–15]. The consensus problem of high-order agent systems is discussed in [16]. The robustness of consensus in single integrator multiagent systems to coupling delays and switching topologies is investigated [17, 18]. Actually, more researchers are interested in solving the robust consensus problem with both delays and disturbances;
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