A Phase Theory of Multi-Input Multi-Output Linear Time-Invariant Systems

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-04-08 DOI:10.1137/22m148968x

Wei Chen, Dan Wang, Sei Zhen Khong, Li Qiu

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1235-1260, April 2024.
Abstract. In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase subsumes the well-known notion of positive real systems and is closely related to the notion of negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time-domain interpretations of phase-bounded systems via both energy signal analysis and power signal analysis.

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多输入多输出线性时不变系统的相位理论

SIAM 控制与优化期刊》第 62 卷第 2 期第 1235-1260 页，2024 年 4 月。摘要本文定义了一类多输入多输出（MIMO）线性时不变（LTI）系统的相位响应，该系统的频率响应在所有频率上均为（半）扇形。新定义的相位包含众所周知的正实系统概念，并与负虚系统概念密切相关。我们提出了反馈稳定性的小相位定理，它是对小增益定理的补充。小相位定理为多输入多输出系统的相位理论奠定了基础。我们还通过能量信号分析和功率信号分析讨论了相位约束系统的时域解释。

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.