Abstract:This paper investigates the consensus problem of general linear multi-agent systems under the directed topology, and proposes a novel protocol based on the distributed PID control law. Firstly, through state transformation. The, consensus problem is transformed into an asymptotic stability problem of an error system, then the Lyapunov functional is constructed and the sufficient condition for consensus is given based on the linear matrix inequation(LMI). Finally, the comparisons with pure proportional control through simulation are made. The simulations results show that if the topology contains a globally reachable node, appropriate PID parameters can overcome the impact of the noise and shorten the convergence time.