Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems
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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 wordsAverage dwell time Impulse Exponential stability Robustness
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- Hespanha, J.P., Morse, A.S., 1999. Stability of switched systems with average dwell-time. Proc. 38th IEEE Conf. on Decision and Control, p.2655–2660. [doi:10.1109/CDC.1999.831330]Google Scholar
- Hiskens, I.A., 2001. Stability of hybrid system limit cycles: application to the compass gait biped robot. Proc. 40th IEEE Conf. on Decision and Control, p.774–779. [doi:10.1109/.2001.980200]Google Scholar
- Qin, S.Y., Song, Y.H., 2001. The theory of hybrid control systems and its application perspective in electric power systems. Proc. Int. Conf. on Info-Tech and Info-Net, p.85–94. [doi:10.1109/ICII.2001.983729]Google Scholar
- Sun, X.M., Wang, D., Wang, W., et al., 2007. Stability analysis and L2-gain of switched delay systems with stable and unstable subsystems. IEEE 22nd Int. Symp. on Intelligent Control, p.208–213. [doi:10.1109/ISIC.2007.4450886]Google Scholar
- Wang, M., Dimirovski, G.M., Zhao, J., 2008. Average dwell-time method to stabilization and L2-gain analysis for uncertain switched nonlinear systems. Proc. 17th IFAC World Congress, p.7642–7647. [doi:10.3182/20080706-5-KR-1001.01292]Google Scholar