How do the lengths of switching intervals influence the stability of a dynamical system?

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

Automatica Pub Date : 2024-10-04 DOI:10.1016/j.automatica.2024.111929

Vladimir Yu. Protasov , Rinat Kamalov

引用次数: 0

Abstract

If a linear switching system with frequent switches is stable, will it be stable under arbitrary switches? In general, the answer is negative. Nevertheless, this question can be answered in an explicit form for any concrete system. This is done by finding the mode-dependent critical lengths of switching intervals after which any enlargement does not influence the stability. The solution is given in terms of the exponential polynomials of least deviation from zero on a segment (“Chebyshev-like” polynomials). By proving several theoretical results on exponential polynomial approximation we derive an algorithm for finding such polynomials and for computing the critical switching time. The convergence of the algorithm is estimated and numerical results are provided.

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切换间隔的长度如何影响动力系统的稳定性？

如果一个频繁开关的线性开关系统是稳定的，那么它在任意开关下也会稳定吗？一般来说，答案是否定的。不过，对于任何具体系统，这个问题都可以用明确的形式来回答。具体方法是找到与模式相关的开关间隔临界长度，在此临界长度之后，任何开关间隔的扩大都不会影响稳定性。求解方法是根据线段上偏离零点最小的指数多项式（"类切比雪夫 "多项式）给出的。通过证明指数多项式近似的几个理论结果，我们推导出一种算法，用于寻找此类多项式和计算临界切换时间。对算法的收敛性进行了估计，并提供了数值结果。

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.