Abstract This paper is concerned with leader-following consensus of general linear multi-agent systems with random switching topologies, where the dwell time in each topology consists of a fixed part and random part, and the topology switching signal in random part is modeled by a semi-markov process. First, a semi-Markov switched system with state jumps is constructed, and the stochastic stability of the constructed system is shown to be equivalent to that of the original system. Then a necessary and sufficient condition is established by using a Lyapunov approach in terms of linear matrix inequalities. Finally, the effectiveness of our results is illustrated by a numerical example and a practical example.

中文翻译：

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随机切换拓扑多智能体系统领导者跟随共识的充要条件

摘要 本文研究具有随机切换拓扑的一般线性多智能体系统的领导者跟随共识，其中每个拓扑中的停留时间由固定部分和随机部分组成，随机部分的拓扑切换信号由半马尔可夫过程。首先，构造了一个具有状态跳跃的半马尔可夫切换系统，并证明了所构造系统的随机稳定性与原系统的随机稳定性是等价的。然后利用李雅普诺夫方法根据线性矩阵不等式建立充分必要条件。最后，我们通过一个数值例子和一个实际例子说明了我们结果的有效性。