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.