A Delay Classification-Based Approach to Distributed Consensus of Nonlinear Time-Delay Multiagent Systems

This paper investigates the problem of the fixed directed topology-based leader-following consensus control for nonlinear multiagent systems with output delays. Diverging from existing results, this study focuses on large time-varying output delay. Taking this condition into account, a novel delay classification-based distributed output feedback consensus algorithm is developed. First, we divide the output delay into two types through a designed constant and introduce a switching signal to distinguish these two types. Then, we build a distributed compensator for each follower using relevant outputs to reconstitute the leader-following tracking errors. This compensator relies on the output delay and is irrelevant to the nonlinear dynamics of the system. Then, we design a distributed linear controller for each follower with the compensator's assistance. Subsequently, a new unified Lyapunov-Krasovskii functional is developed to prove that all agents can realize leader-following full-state consensus with the action of the controller. We also provide sufficient conditions to demonstrate the controller's validity. Finally, a simulation example is supplied to validate the efficiency of our algorithm.