Consensus for linear multi-agent systems with constant and time-varying communication delays via delay-decomposition approach

This paper is concerned with the consensus problem of linear multi-agent systems with constant and time-varying communication delays over fixed topology. A proportional and derivative like (PD-like) consensus algorithm is proposed to address the problem, which is available to transform the system into a neutral-like system. By uniformly dividing the delay interval into multiple segments, a Lyapunov-Krasovskii functional constructed to analysis the stability of the system. Then, some new consensus conditions are presented in terms of linear matrix inequality (LMI) to tolerate a large upper bound of the time-delay. Finally, some simulations are provided to demonstrate the effectiveness of the proposed results.