Graph-based necessary and sufficient conditions for exponential stability of switched positive systems with marginally stable subsystems

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-11-22 DOI:10.1016/j.automatica.2024.111989

Jie Lian , Shuang An , Dong Wang

引用次数: 0

Abstract

This paper derives necessary and sufficient (N&S) conditions for the exponential stability of discrete-time switched positive linear systems under transfer-restricted switching. The transfer-restricted switching property is characterized by a switching digraph, and the structural properties for subsystems are characterized by a novel class of state component digraphs. Combining with the two properties, some joint path conditions involving the sum and product matrices of multiple subsystems respectively are presented as N&S conditions based on weak common linear co-positive Lyapunov functions (weak-CLCLFs). The presented conditions allow all subsystems to be marginally stable rather than asymptotically stable. Finally, a simulation example is provided to show the effectiveness and superiority of the proposed method.

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基于图的具有边际稳定子系统的开关正系统指数稳定性的必要条件和充分条件

本文推导了离散时间开关正线性系统在传输受限开关下指数稳定性的必要和充分（N&S）条件。限制转移切换特性由切换数字图表征，子系统的结构特性由一类新的状态分量数字图表征。结合这两个特性，提出了一些分别涉及多个子系统的总和矩阵和乘积矩阵的联合路径条件，作为基于弱共线性共正李亚普诺夫函数（weak-CLCLFs）的 N&S 条件。提出的条件允许所有子系统保持边际稳定，而不是渐近稳定。最后，我们提供了一个仿真实例，以说明所提方法的有效性和优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.