On Converse Lyapunov Theorem for Fixed-Time Input-to-State Stability

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-01-12 DOI:10.1137/22m1497596

Denis Efimov, Andrey Polyakov

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 118-134, February 2024.
Abstract. Input-to-state stability is one of the most utilizable robust stability properties for nonlinear dynamical systems, while (nearly) fixed-time convergence is a kind of decay for trajectories of disturbance-free systems that is independent in initial conditions. The presence of both these features for a system can be checked by the existence of a proper Lyapunov function. The objective of this work is to provide the conditions for a converse result that (nearly) fixed-time input-to-state stable systems admit a respective Lyapunov function. Similar auxiliary results for uniform finite-time stability and uniform (nearly) fixed-time stability are obtained.

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论固定时间输入到状态稳定性的逆 Lyapunov 定理

SIAM 控制与优化期刊》第 62 卷第 1 期第 118-134 页，2024 年 2 月。摘要输入到状态稳定性是非线性动力系统最常用的鲁棒稳定性特性之一，而（近似）固定时间收敛是无扰动系统轨迹的一种衰减，与初始条件无关。系统是否具有这两个特性，可以通过是否存在适当的 Lyapunov 函数来检验。这项工作的目的是为反向结果提供条件，即（近）固定时间输入到状态稳定系统承认各自的 Lyapunov 函数。我们还得到了均匀有限时间稳定性和均匀（近）固定时间稳定性的类似辅助结果。

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

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.