Control design method based on nonsmooth switching surfaces

A control design method based on nonsmooth switching surfaces is proposed for a class of second-order systems in order to enhance the flexibility of system design. Firstly, the self-stable region(SSR) with linear Lipschitz boundary surfaces is constructed by utilizing the notion of SSR. Then, the control law is derived and the convergence of the closed-loop system is proved by the contingent cone criteria, which is used to determine the relation between the solution of a differential equation and a nonsmooth surface. The results show that the control design method developed in this paper allows us to construct the SSR in a more general sense, and the flexibility of system design can be improved. Finally, the correctness and effectiveness of the control design method presented are illustrated by a numerical example.