Sliding mode control design based on new approaching criteria for linear Lipschitz switching surface

A new design method of sliding mode control (SMC) is proposed to generalize the conversional procedure which is usually based on Filippov´s approaching conditions for only smooth surface. As the fundamental result, the new approaching criteria are developed to show the sufficient conditions on the relation between the trajectories and a nonsmooth surface in state space, if the dynamics of the trajectories can be described by Filippov´s differential inclusion. According to the new approaching criteria, the approaching phase design of SMC can be relaxed, through the switching surface may be nonsmooth. Furthermore, for a class of nonlinear single-input single-output (SISO) systems, the sliding mode controller with a linear Lipschitz continuous switching surface can be systemically designed. From the viewpoint of SMC, it provides a new path to realize the different requirements of the sliding motion according to the partitioned regions.