Sliding mode control design with Lipschitz switching surfaces for uncertain systems

In this paper, a slidingmode control (SMC) method for a class of nonlinear uncertain systems is proposed based on the newcontingent cone criteria, which is utilized to estimate the relation between the phase trajectories and an arbitrary Lipschitz continuous surface. A Lipschitz continuous sliding surface is constructed and a feedback controller is designed to drive the trajectories of the closed-loop system to the surface in finite time. The asymptotic convergence property to the origin is proved based on a series of Lipschitz domains constructed recursively, each of which contains two Lipschitz switching surfaces that may be nonsmooth. Filippov´s differential inclusion is adopted to describe the dynamics of the closed-loop system. Finally, the validity of the method is illuminated by a 3-dimensional numerical example.