Consensus of Multiagent Systems With Time-Varying Delays and Switching Topologies Based on Delay-Product-Type Functionals

This article investigates the consensus problem of multiagent systems (MASs) with time-varying delays subject to switching topologies. For the purpose of obtaining less conservative consensus conditions, first, a delay-product-type Lyapunov–Krasovskii functional (LKF) based on the auxiliary function-based integral inequality (AFBII) is constructed. Then, the generalized reciprocally convex matrix inequality (GRCMI) and a relaxed quadratic function negative-determination lemma are introduced to obtain the maximal-allowable upper bound of time-varying delays. Moreover, a proportional and derivative-like (PD-like) protocol is designed and the result is extended to the leader-following consensus of agents under Lipschitz nonlinear dynamics. Finally, two illustrative examples, including Chua’s circuit, are given to demonstrate the advantages of the new consensus criteria.