PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

doi:10.1016/S0252-9602(17)30005-X

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 329-341.doi: 10.1016/S0252-9602(17)30005-X

PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

Alexander ALEKSANDROV¹, Elena ALEKSANDROVA¹, Alexey ZHABKO¹, 陈阳舟²

1. Saint Petersburg State University, Saint Petersburg 199034, Russia;
2. Beijing Key Laboratory of Transportation Engineering, College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China

收稿日期:2016-10-06 修回日期:2016-07-10 出版日期:2017-04-25 发布日期:2017-04-25
通讯作者: Yangzhou CHEN,E-mail:yzchen@bjut.edu.cn E-mail:yzchen@bjut.edu.cn
作者简介:Alexander ALEKSANDROV,E-mail:a.u.aleksandrov@spbu.ru;Elena ALEKSANDROVA,e.aleksandrova@spbu.ru;Alexey ZHABKO,a.zhabko@spbu.ru;Yangzhou CHEN,E-mail:yzchen@bjut.edu.cn
基金资助:
The research was supported by the Saint Petersburg State University (9.42.1045.2016), the Russian Foundation for Basic Research (15-58-53017 and 16-01-00587), and the Natural Science Foundation of China (6141101096, 61573030, and 61273006).

PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

Alexander ALEKSANDROV¹, Elena ALEKSANDROVA¹, Alexey ZHABKO¹, Yangzhou CHEN²

1. Saint Petersburg State University, Saint Petersburg 199034, Russia;
2. Beijing Key Laboratory of Transportation Engineering, College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China

Received:2016-10-06 Revised:2016-07-10 Online:2017-04-25 Published:2017-04-25
Contact: Yangzhou CHEN,E-mail:yzchen@bjut.edu.cn E-mail:yzchen@bjut.edu.cn
Supported by:
The research was supported by the Saint Petersburg State University (9.42.1045.2016), the Russian Foundation for Basic Research (15-58-53017 and 16-01-00587), and the Natural Science Foundation of China (6141101096, 61573030, and 61273006).

摘要/Abstract

摘要：

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

关键词: Nonlinear systems, partial asymptotic stability, Lyapunov function, sector nonlinearities, time-delay

Abstract:

Key words: Nonlinear systems, partial asymptotic stability, Lyapunov function, sector nonlinearities, time-delay

Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, 陈阳舟. PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS[J]. 数学物理学报(英文版), 2017, 37(2): 329-341.

Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, Yangzhou CHEN. PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS[J]. Acta mathematica scientia,Series B, 2017, 37(2): 329-341.

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PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

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