Sliding mode control for a class of second-order systems via linear Lipschitz surfaces

In order to improve flexibility of sliding mode control for a class of second-order systems, a new control design method is proposed in this paper. The sliding surface is designed to be a linear Lipschitz continuous surface instead of a smooth one. Due to the nonsmoothness of the sliding surface, the control design problem is discussed in the framework of Filippov´s differential inclusion and nonsmooth analysis, by utilizing Clarke´s generalized gradient. The stability of the constructed piecewise linear sliding surface is analyzed, and the trajectories of the closed-loop system are steered to the sliding surface in finite time with the discontinuous control law. The effectiveness of our design is illustrated by a numerical example.