时变动力系统稳定性新准则:在弹簧-质量-阻尼器模型中的应用

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-02-01 DOI:10.1016/S0034-4877(23)00007-1

Ezzine Faten, Mohamed Ali Hammami

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引用次数: 0

摘要

本文研究了一类非线性时变系统关于部分变量的稳定性问题。基于李雅普诺夫技术，给出了摄动系统部分变量指数稳定和实际指数稳定的充分条件，并给出了逆定理。此外，还提供了一些例子来说明稳定性理论对于部分变量的有用性和适用性。特别地，我们证明了我们的方法可以应用于弹簧-质量-阻尼器模型。

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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NEW CRITERION OF STABILITY FOR TIME-VARYING DYNAMICAL SYSTEMS: APPLICATION TO SPRING-MASS-DAMPER MODEL

In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.