Nonsmooth control design of mechanical systems with friction in the sense of Filippov

Utilizing the notion of Filippov solution, a sliding mode control law is derived for generic second order nonlinear mechanical system with friction. The control law is designed with some tunable parameters and optional functions. The asymptotically stability of the closed-loop system is proved by the concept of the solution, nonsmooth analysis and nonsmooth Lyapunov stability theory. By some numerical examples, the correctness of the control law is illuminated. Finally, the validity of the controller design is verified by a simulation example for a flight simulation table system with Stricbeck friction model.