Leader–follower consensus of nonlinear time-delay multiagent systems: A time-varying gain approach

In this paper, the leader–follower consensus problem is investigated for feedforward nonlinear time-delay multiagent systems under a fixed directed topology. A novel static low-gain observer is first proposed for each follower by only utilizing the output information of the follower and its neighbor agents. Based on an appropriate state transformation, the distributed output feedback controller with a static gain is then designed for each follower such that the consensus of the multiagent system is achieved. It is however noted that under the static gain controllers, the consensus convergence speed is slow and transient performance leaves much to be desired. To improve performance of the consensus protocol, the distributed output feedback controllers with bounded time-varying gains are further designed. It is shown that the proposed time-varying gain approach plays a significant role in improving the convergence speed and transient performance of the distributed consensus protocol. Through a simulation example, the effectiveness of the proposed consensus protocol is illustrated, and the advantages of the proposed time-varying gain approach are also demonstrated.