Journal of Zhejiang University SCIENCE C

, Volume 15, Issue 1, pp 31–42 | Cite as

Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems



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 

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Information Science and TechnologyXiamen UniversityXiamenChina

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