Consensus Problem of First-order Multi-agent Systems with Communication Delay and Input Delay

Consensus problem is investigated for the first-order multi-agent system with time-varying communication delay and time invariant input delay.With the assumption that each node in the interconnection topology has the same out-degree, the consensus problem of the multi-agent system is converted into the asymptotical stability problem of a reduced-order system by adopting the variable transformation.Based on Lyapunov asymptotical stability theorem and linear matrix inequality(LMI) method,sufficient conditions,which are dependent on both the communication delay and input delay,are obtained for the multi-agent system with static and connected interconnection topology converging to a consensus when the derivative information of the communication delay is given and unknown respectively.Simulation results illustrate the effectiveness of the conclusion.