Considering the network restrictions such as multiple time-varying delays, disturbances with limited energy and
time-varying topologies uncertainties, the delay-dependent stability criteria for robust consensus of multi-agent systems
are proposed. Firstly, by using the idea of state decomposition, the condition for guaranteeing robust consensus is
converted into verifying the robust stability of the disagreement systems. Considering multiple time-varying delays and
switching topologies, Lyapunov-Krasovskii functional is constructed to analyse the robust stability. By using free-weighting
matrices(FWM) method, the stability criteria can be obtained through solving the corresponding feasible nonlinear matrix
inequality nonlinear matrix inequality(NLMI). Finally, according to solving cone complementarity problem, nonlinear
minimization is employed to obtain the LMI criteria with lower conservativeness and be solved easily. Numerical examples
and simulation results show the effectiveness of the proposed criteria.