有稳定和不稳定子系统的非线性脉冲切换系统的指数稳定性

Xiao-li ZHANG; An-hui LIN; Jian-ping ZENG

doi:10.1631/jzus.C1300123

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有稳定和不稳定子系统的非线性脉冲切换系统的指数稳定性

计算机与自动化 | Updated：2022-05-19

- 有稳定和不稳定子系统的非线性脉冲切换系统的指数稳定性
- Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems
- 信息与电子工程前沿（英文） 2014年15卷第1期页码：31-42
- Affiliations：
  
  School of Information Science and Technology, Xiamen University, Xiamen 361005, China
- Author bio：
  
  Xiao-li ZHANG, E-mail: zhxl@xmu.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61074004 and 61374037)
- DOI：10.1631/jzus.C1300123
  中图分类号： TP13
- 收稿：2013-05-09，
  
  修回：2013-12-16，
  
  纸质出版：2014-01
- Accepted：
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有稳定和不稳定子系统的非线性脉冲切换系统的指数稳定性[J]. 信息与电子工程前沿（英文）, 2014,15(1):31-42.

Xiao-li ZHANG, An-hui LIN, Jian-ping ZENG. Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(1): 31-42.
有稳定和不稳定子系统的非线性脉冲切换系统的指数稳定性[J]. 信息与电子工程前沿（英文）, 2014,15(1):31-42. DOI： 10.1631/jzus.C1300123.

Xiao-li ZHANG, An-hui LIN, Jian-ping ZENG. Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(1): 31-42. DOI： 10.1631/jzus.C1300123.

摘要

研究目的

对一类同时包含稳定和不稳定子系统的切换非线性系统的稳定性及鲁棒稳定性进行研究。旨在针对在切换时刻包含非线性脉冲

且每个子系统都具有非线性级联形式的切换非线性系统

给出其稳定的充分条件

为此类系统的稳定性问题研究提供理论依据。

重要结论

将在切换线性系统切换时刻的非线性脉冲处理方法和手段推广至切换非线性系统中。在应用非线性系统的Lyapunov函数处理非线性脉冲时

适当地利用了矩阵不等式的相关方法。当不稳定子系统和稳定子系统的活跃时间小于一定比例

并且在切换时刻存在满足相应界的非线性脉冲时

切换非线性系统仍能保持其指数稳定性。在不确定性满足相应界的条件下

切换非线性系统也能保持其鲁棒指数稳定性。

Abstract

Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. At each switching time instant

the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. Using the average dwell time method and piecewise Lyapunov function approach

when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion

the exponential stability of the switched system is guaranteed. The switching law is designed which includes the average dwell time of the switched system. Switched systems with uncertainties are also studied. Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems. Finally

simulations show the effectiveness of the result.

关键词

Keywords

references

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