Please wait a minute...
FITEE
Front. Inform. Technol. Electron. Eng.  2014, Vol. 15 Issue (1): 31-42    DOI: 10.1631/jzus.C1300123
    
Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems
Xiao-li Zhang, An-hui Lin, Jian-ping Zeng
School of Information Science and Technology, Xiamen University, Xiamen 361005, China
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

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.

Key words： Average dwell time      Impulse      Exponential stability      Robustness     
Received: 09 May 2013      Published: 07 January 2014
CLC:  TP13  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Xiao-li Zhang
An-hui Lin
Jian-ping Zeng
Cite this article:

Xiao-li Zhang, An-hui Lin, Jian-ping Zeng. Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems. Front. Inform. Technol. Electron. Eng., 2014, 15(1): 31-42.

URL:

http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1300123     OR     http://www.zjujournals.com/xueshu/fitee/Y2014/V15/I1/31


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

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。
[1] Lin CAO , Shuo TANG , Dong ZHANG. Flight control for air-breathing hypersonic vehicles using linear quadratic regulator design based on stochastic robustness analysis[J]. Front. Inform. Technol. Electron. Eng., 2017, 18(7): 882-897.
[2] Jing-ming KUANG, Yuan ZHOU, Ze-song FEI. Joint DOA and channel estimation with data detection based on 2D unitary ESPRIT in massive MIMO systems   [J]. Front. Inform. Technol. Electron. Eng., 2017, 18(6): 841-849.
[3] Wei Xia, Ju-lei Zhu, Wen-ying Jiang, Ling-feng Zhu. An enhanced mixed modulated Lagrange explicit time delay estimator with noisy input[J]. Front. Inform. Technol. Electron. Eng., 2016, 17(10): 1067-1073.
[4] Hao Zhou, Yin-fei Zheng. An efficient quadrature demodulator for medical ultrasound imaging[J]. Front. Inform. Technol. Electron. Eng., 2015, 16(4): 301-310.
[5] Xiao-hua Wang, Juan-juan Yu, Yao Huang, Hua Wang, Zhong-hua Miao. Adaptive dynamic programming for linear impulse systems[J]. Front. Inform. Technol. Electron. Eng., 2014, 15(1): 43-50.
[6] Xiang Pan, Jian-long Li, Wen Xu, Xian-yi Gong. Robust time reversal processing for active detection of a small bottom target in a shallow water waveguide[J]. Front. Inform. Technol. Electron. Eng., 2010, 11(5): 401-406.
[7] Chang-cheng WU, Chun-yu ZHAO, Da-yue CHEN. Improved switching based filter for protecting thin lines of color images[J]. Front. Inform. Technol. Electron. Eng., 2010, 11(1): 36-44.