Sliding Mode Control for a Class of Systems based on a Non-Monotonic Lyapunov Function

This article discusses the sliding mode control problem, where the reaching phase is achieved non-monotonically, and the sliding phase can be achieved either monotonically or non-monotonically. Once the reaching phase is completed, the state variables slide on the sliding manifold and then reach the equilibrium point. A practical second-order example of the ball motion model is considered to show the non-monotonic reaching phase. Simulation results verify the non-monotonic behavior of the reaching phase.