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 developped 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.