Second-order uniform exact sliding mode control with uniform sliding surface

In this paper we propose an uniform sliding mode controller for a second order uncertain system providing convergence to an arbitrary small vicinity of origin in finite time, which can be bounded by some constant independent from initial conditions and uncertainties. With this aim a nonlinear sliding surface is proposed ensuring during the sliding motions an uniform convergence of the trajectories to any arbitrary small vicinity of origin in finite time bounded by some constant independent from initial conditions on the surface.