Impulsive switching signals with functional inequalities: Stability analysis using hybrid systems framework

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Automatica Pub Date : 2024-09-27 DOI:10.1016/j.automatica.2024.111928

Shenyu Liu , Aneel Tanwani

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引用次数: 0

Abstract

In this work, we introduce a class of impulsive switching signals described via functional inequalities which govern the switching among different modes with state resets. By choosing the parameters of the inequalities appropriately, we can recover several known classes of switching signals and also allow for signals that depend on time, mode or state of the system. Signals from this class can also be generated online via the use of an auxiliary timer while the dynamical system is running. Via a multiple Lyapunov functions approach, we provide sufficient conditions on the functional parameters of the switching signal which ensure that the equilibrium is globally asymptotically stable (GAS) for autonomous impulsive switched system. In case of inputs, similar methodology is used to provide sufficient conditions for input-to-state stability (ISS) and integral-input-to-state stability (iISS) uniformly over the proposed class of impulsive switching signals. As case studies, we consider switched systems which do not satisfy ISS (respectively, iISS) property for switching signals with arbitrarily large dwell-times but they are shown to be ISS (resp. iISS) for our proposed class of impulsive switchings signals described via functional inequalities.

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带函数不等式的脉冲开关信号：利用混合系统框架进行稳定性分析

在这项研究中，我们引入了一类通过函数不等式描述的脉冲切换信号，这些信号控制着不同模式间的切换和状态重置。通过适当选择不等式的参数，我们可以恢复几类已知的开关信号，并允许信号取决于系统的时间、模式或状态。这类信号也可以在动力系统运行时通过使用辅助计时器在线生成。通过多重 Lyapunov 函数方法，我们提供了开关信号函数参数的充分条件，确保自主脉冲开关系统的平衡是全局渐近稳定的（GAS）。在输入方面，我们使用类似的方法为输入到状态稳定性（ISS）和积分输入到状态稳定性（iISS）提供了充分条件，这些充分条件在所提出的脉冲开关信号类别中是一致的。作为案例研究，我们考虑了对于具有任意大停留时间的开关信号不满足 ISS（分别为 iISS）特性的开关系统，但对于我们提出的通过函数不等式描述的脉冲开关信号类别，这些系统被证明是 ISS（分别为 iISS）的。

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.