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.

中文翻译：

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时变时滞多智能体系统共识及基于时滞积型泛函的切换拓扑


本文研究了具有受切换拓扑影响的时变延迟的多智能体系统 (MAS) 的共识问题。为了获得不太保守的共识条件，首先，构造基于辅助函数的积分不等式（AFBII）的延迟积型Lyapunov-Krasovskii泛函（LKF）。然后，引入广义倒数凸矩阵不等式（GRCMI）和松弛二次函数负定引理来获得时变延迟的最大允许上限。此外，设计了比例导数类（PD-like）协议，并将结果扩展到Lipschitz非线性动力学下代理的领导者跟随共识。最后，给出了两个说明性示例（包括 Chua 电路）来展示新共识标准的优势。