ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1921-1938.

ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

薛焕斌¹, 张继业²

1 College of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China;
2 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

收稿日期:2017-03-28 修回日期:2018-02-07 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Huanbin XUE E-mail:huanbinxue@163.com
作者简介:Jiye ZHANG,E-mail:jyzhang@home.swjtu.edu.cn
基金资助:
This research was supported by the Natural Science Foundation of China (11572264), the Foundation for Distinguished Young Talents in Higher Education of Guangdong (2016KQNCX103).

ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

Huanbin XUE¹, Jiye ZHANG²

1 College of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China;
2 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

Received:2017-03-28 Revised:2018-02-07 Online:2018-12-25 Published:2018-12-28
Contact: Huanbin XUE E-mail:huanbinxue@163.com
Supported by:
This research was supported by the Natural Science Foundation of China (11572264), the Foundation for Distinguished Young Talents in Higher Education of Guangdong (2016KQNCX103).

摘要/Abstract

摘要： The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.

关键词: interconnected systems, robust stability, switching rule, unbounded delay

Abstract: The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.

Key words: interconnected systems, robust stability, switching rule, unbounded delay

薛焕斌, 张继业. ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING[J]. 数学物理学报(英文版), 2018, 38(6): 1921-1938.

Huanbin XUE, Jiye ZHANG. ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1921-1938.

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ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

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