其唯一巴拉巴诺夫规范并非严格凸形的不可还原线性开关系统

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-01-10 DOI:10.1137/23m1551213

Ian D. Morris

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 1 期第 42-64 页，2024 年 2 月。摘要我们构造了一个连续时间、四维、有三个切换状态的边际稳定线性切换系统，该系统相对于恒定切换定律是指数稳定的，且具有唯一的巴拉巴诺夫规范，但巴拉巴诺夫规范不是严格凸的。这解决了奇图尔、盖伊和梅森的一个问题。

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An Irreducible Linear Switching System Whose Unique Barabanov Norm Is Not Strictly Convex

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 42-64, February 2024.
Abstract. We construct a marginally stable linear switching system in continuous time, in four dimensions, and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm, but such that the Barabanov norm fails to be strictly convex. This resolves a question of Chitour, Gaye, and Mason.

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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.