This paper discusses the average consensus problem of multi-agent systems with multiple communication delays.
The stability criteria of the network dynamic is analyzed by constructing Lyapunov-Krasovskii function, and the tolerant
upper bounds of communication delays can be obtained through solving feasible linear matrix inequalities(LMIs). In order
to relax the conservativeness, free-weighting matrices method is employed in the main results. Numerical examples and
simulations results show the effectiveness of the proposed method.