Control design of a class of uncertain second-order systems via SSR and contingent cone criteria

By utilizing the notion of self-stable region (SSR), a SSR with linear Lipschitz surface boundary is constructed for a class of uncertain second-order systems. A control law is proposed based on the constructed SSR, Filippov solution and contingent cone criteria, which is attached to nonsmooth analysis. It is proved that the trajectories of the closed-loop system reach the boundary of the SSR and enter into its interior in finite time, then converge to the origin by the notion of SSR. Through the results, the SSR can be constructed in a more general sense, which improves the flexibility of the control design. Finally, the simulation results show the correction and effectiveness of the design.