Stabilisation and L₂-gain analysis for a class of uncertain switched non-linear systems

Abstract

This article is concerned with the problem of stabilisation and L ₂-gain analysis for a class of switched non-linear systems with norm-bounded time-varying uncertainties. A system in this class is composed of two parts: an uncertain linear switched part and a non-linear part, which are also switched systems. When all the subsystems are stabilisable and have an L ₂-gain, the switched feedback control law and the switching law are designed respectively using average dwell-time method such that the corresponding closed-loop switched system is exponentially stable and achieves a weighted L ₂-gain.

Keywords:

• switching systems
• H-infinity control
• switched non-linear cascade systems
• exponential stability
• piecewise Lyapunov function
• average dwell-time method
• L ₂-gain

Acknowledgements

This work was supported by Dogus University Fund for Science, the NSFC under Grants 60874024 and 90816028 and the SRFDP under Grant 200801450019.