This study focuses on mixed time delayed, both leaderless and leader-follower problems of nonlinear multi-agent systems. Here, we find the stability criteria for multi-agent systems (MASs) by utilizing a proposed lemma, the Lyapunov–Krasovskii functions, analytical techniques, Kronecker product, and some general specifications to obtain the asymptotic stability for the constructed MASs. Furthermore, the criteria to establish the synchronization of leader-follower multiagent systems with linear feedback controllers are discussed. Finally, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported for both leaderless and leader-follower problem in this study.

中文翻译：

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具有混合时滞的非线性多Agent系统的稳定性和线性反馈同步控制的Lyapunov–Krasovskii函数方法

这项研究的重点是非线性多主体系统的混合时间延迟，无领导者和领导者跟随者问题。在这里，我们通过利用提出的引理，Lyapunov–Krasovskii函数，分析技术，Kronecker乘积和一些一般性规范来找到多智能体系统（MAS）的稳定性标准，以获取所构造MAS的渐近稳定性。此外，讨论了建立具有线性反馈控制器的跟随者多主体系统同步的标准。最后，我们提供了两个数值计算以及计算仿真，以检查针对本研究中无领导者和领导者跟随者问题所报告的理论发现的有效性。