Fast second-order Sliding Mode Control design based on Lyapunov function

We design a new kind of fast terminal sliding mode controller for second-order uncertain systems with a single control input. In contrast to the reported techniques, which are based on the Terminal Sliding Mode Control, the proposed controller design is based on Lyapunov methods. Sufficient conditions are given to ensure the finite-time stability of the close-loop system with the proposed discontinuous controller. The performance is compared with others Fast Terminal Sliding Mode controllers by means of a simulation example.