New results on robust control for a class of uncertain systems and its applications to Chua’s oscillator

Abstract

This paper addresses the problems of robust stability analysis and stabilization for continuous-time systems with state-dependent uncertainties via constructing a new parameter-dependent Lyapunov function. On the basis of such a parameter-dependent Lyapunov function, the stability conditions for open-loop uncertain systems are first presented. Then a relaxed stability analysis approach that utilizes a property of the time derivatives of uncertain parameters is obtained. To take full advantage of the parameter-dependent Lyapunov function, a model-dependent state-feedback stabilization scheme is proposed, which can provide more flexibilities in controller synthesis. The static state-feedback controller can be seen as a special case of the model-dependent state-feedback controller. A numerical example is provided to illustrate the effectiveness of the proposed approaches. Finally, the developed controller design methodology is applied to stabilization and synchronization of Chua’s oscillator, which has wide applications in secure communication systems and power electronic systems.