Control design with Lipschitz switching surfaces based on new contingent cone criteria

In this paper, a control design method for a class of non-linear uncertain systems is proposed based on the new contingent cone criteria, which are used to estimate the relation between the phase trajectories and an arbitrary Lipschitz continuous surface. A series of Lipschitz domains are constructed recursively, each of which contains two Lipschitz switching surfaces that may be non-smooth. Filippov's differential inclusion is adopted to describe the dynamics of the closed-loop system. Based on the constructed Lipschitz domains, a feedback controller is designed to drive the trajectories of the closed-loop system to the origin asymptotically. Finally, the validity of the method is illuminated by some numerical examples.