二维离散时间线性开关系统的稳定性二分法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-01-31 DOI:10.1137/23m1551225

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 400-414 页，2024 年 2 月。摘要我们证明，对于每一个具有有限多个切换状态的双复变离散时间线性切换系统，要么系统是李亚普诺夫稳定的，要么存在一个至少以线性速度逃逸到无穷远的轨迹。我们还给出了一个可检查的代数准则来区分这两种情况。这种二分法以前已知在两个实变系统中成立，但已知在更高维度和具有无限多切换状态的系统中是错误的。

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A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 400-414, February 2024.
Abstract. We prove that, for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear speed. We also give a checkable algebraic criterion to distinguish these two cases. This dichotomy was previously known to hold for systems in two real variables but is known to be false in higher dimensions and for systems with infinitely many switching states.

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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.