Abstract In this paper, the problem of non-fragile guaranteed-performance H ∞ leader-following consensus protocol design for high-order multi-agent systems with Lipschitz nonlinearities and switching topologies is investigated. The communication interactions among all agents are described by a set of switching directed graphs, whose union contains a directed spanning tree rooting at the leader node. By constructing a nonsingular transformation, leader-following consensus of the concerned multi-agent system is transformed into the problem of asymptotic stability analysis for some consensus error systems. Taking into account the existences of exogenous disturbances in practical agent systems and gain perturbations in physical controller implementations, the non-fragile H ∞ criterion is introduced not only to design the consensus protocol which is capable of tolerating some level of parametric uncertainties, but also to make the consensus error system asymptotically stable with a prescribed H ∞ disturbance attenuation level. To regulate the consensus performance, a quadratic function collecting consensus errors among in-neighboring agents is proposed. By employing tools from algebraic graph theory and Lyapunov functional technique, sufficient conditions on the desired consensus protocol design are derived in terms of linear matrix inequalities. Simulation illustrates the effectiveness of the theoretical results.

中文翻译：

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具有切换拓扑的 Lipschitz 非线性多智能体系统的非脆弱保证性能 H∞ 领导者跟随共识

摘要 在本文中，研究了具有Lipschitz 非线性和切换拓扑的高阶多智能体系统的非脆弱保证性能H ∞ 领导者跟随共识协议设计问题。所有代理之间的通信交互由一组切换有向图描述，其并包含以领导节点为根的有向生成树。通过构造一个非奇异变换，将有关多智能体系统的领导者跟随共识转化为一些共识错误系统的渐近稳定性分析问题。考虑到实际代理系统中外生干扰的存在和物理控制器实现中的增益扰动，引入非脆弱 H ∞ 准则不仅是为了设计能够容忍一定程度的参数不确定性的共识协议，而且还使共识误差系统在规定的 H ∞ 干扰衰减水平下渐近稳定。为了调节共识性能，提出了一个收集相邻代理之间共识错误的二次函数。通过使用代数图论和李雅普诺夫函数技术的工具，根据线性矩阵不等式推导出所需共识协议设计的充分条件。仿真说明了理论结果的有效性。为了调节共识性能，提出了一个收集相邻代理之间共识错误的二次函数。通过使用代数图论和李雅普诺夫函数技术的工具，根据线性矩阵不等式推导出所需共识协议设计的充分条件。仿真说明了理论结果的有效性。为了调节共识性能，提出了一个收集相邻代理之间共识错误的二次函数。通过使用代数图论和李雅普诺夫泛函技术的工具，根据线性矩阵不等式推导出所需共识协议设计的充分条件。仿真说明了理论结果的有效性。