Quasi-continuous high-order sliding-mode controllers

A universal finite-time-convergent controller is developed capable to control the output of any uncertain single-input-single-output system with a known permanent relative degree r. The tracking error a is steered to zero by means of a control dependent only on sigma, sigma,..., sigma((r-1)) and continuous everywhere except the set sigma = sigma = ... = sigma((r-1)) = 0. A robust output-feedback controller version provides for the tracking accuracy proportional to the sampling noise magnitude.