In this paper, the distributed finite-time control problem for the class of systems interconnected over an undirected graph is considered. First, the concepts of well-posedness, finite-time boundedness, and contractiveness for the considered systems are given. Then, a sufficient condition is developed to ensure that the plant is well-posed, finite-time bounded, and contractive, where the results are stated by terms of linear matrix inequalities (LMIs). For the control synthesis, we construct a distributed dynamic output-feedback controller inheriting the structure of the plant such that the resulting closed-loop system is finite-time bounded and contractive. Since the analysis condition of the plant used for the closed-loop system is presented by some nonlinear inequalities in given finite-time interval, we further derive a sufficient condition in terms of LMIs with some fixed parameter for the existence of an appropriate output-feedback controller such that the closed-loop system is contractive. Finally, numerical simulations are provided to show the validity of the proposed results.

中文翻译：

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无向图互连系统的分布式有限时间控制

在本文中，考虑了在无向图上互连的系统类的分布式有限时间控制问题。首先，给出了所考虑系统的适定性、有限时间有界性和收缩性的概念。然后，开发了一个充分条件以确保植物是适定的、有限时间有界的和收缩的，其中结果由线性矩阵不等式 (LMI) 表示。对于控制综合，我们构建了一个分布式动态输出反馈控制器，继承了工厂的结构，使得所得到的闭环系统是有限时间有界和收缩的。由于用于闭环系统的被控对象的分析条件由给定有限时间间隔内的一些非线性不等式表示，我们进一步推导出具有一些固定参数的 LMI 的充分条件，用于存在适当的输出反馈控制器，使得闭环系统具有收缩性。最后，提供数值模拟以证明所提出结果的有效性。