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Journal of Zhejiang University SCIENCE C
ISSN 1869-1951(Print), 1869-196x(Online), Monthly
2014 Vol.15 No.1 P.31-42
Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems
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
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。
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DOI:
10.1631/jzus.C1300123
CLC number:
TP13
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On-line Access:
2014-01-07
Received:
2013-05-09
Revision Accepted:
2013-10-22
Crosschecked:
2013-12-16