Asymptotic stabilization in fixed time via sliding mode control

In this note we extend the design of uniform sliding mode controllers for a class of arbitrary order uncertain systems with a single control input. The design is based on the Classical Sliding Mode Control. But, instead of using classical Lipschitz sliding surfaces and relay controllers, we propose a nonlinear sliding surface and two controllers that contain some high degree terms. It allows to enforce the trajectories of the system to a predefined small vicinity centered at the origin in a fixed finite time bounded by some constant independent of the initial conditions and uncertainties.