A new approach to stabilization of uncertain nonlinear systems

This paper presents a new robust stabilization method for a class of uncertain nonlinear systems[UNS] via piecewise linear differential inclusions[PWLDI]. We propose several effective numerical methods for computing the PWLDI to cover the UNS, then present controller design method of obtained PWLDI via piecewise quadratic Lyapunov function to realize robust stability. Because of the inclusion relationship between the obtained PWLDI and original UNS, the obtained controller is also effective to stabilize original UNS. Finally, We demonstrate the proposed design method through a numerical example.

I. INTRODUCTION

The stabilization of uncertain nonlinear systems [UNS] has gained the attention of many researchers in control community. This topic is important since many real-world systems exhibit nonlinear dynamic behavior. To make matters even more difficult, in many practical cases, the mathematical model is poorly known or uncertain. In previous research results, some are the extension of linear system methods, such as Equilibrium Linearization method, exact Linearization via feedback method, while others are the unique methods of the nonlinear systems, such as Lyapunov-based control method, sliding mode control method and robust adaptive control method.