带有可能不稳定成分的抽象互联系统的稳定性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-02-07 DOI:10.1137/23m1572350

Ivan Atamas, Sergey Dashkovskiy, Vitalii Slynko

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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 581-599 页，2024 年 2 月。摘要。从渐近稳定性的角度考虑一维 ODE 与无限维抽象微分方程的相互联系。在整个系统相对于 Minkowski 锥为正的假设下，得到了充分的稳定性条件。解耦 ODE 子系统不要求稳定。我们通过实例来说明我们的结果，展示了所开发的方法相对于现有结果的优势。此外，我们还将我们的结果与已知的小增益理论进行了比较。

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Stability of Abstract Interconnected Systems with a Possibly Unstable Component

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 581-599, February 2024.
Abstract. We consider an interconnection of a one-dimensional ODE and an infinite dimensional abstract differential equation in view of the asymptotic stability. Sufficient stability conditions are obtained under the assumption that the whole system is positive with respect to the Minkowski cone. The decoupled ODE subsystem is not required to be stable. We illustrate our results by means of examples demonstrating the advantages of the developed approach over the existing results. As well we compare our results with the known small-gain theory.

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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.