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 /spl sigma/ is steered to zero by means of a control dependent only on /spl sigma/, /spl sigma//spl dot/, ..., /spl sigma//sup (r-1)/ and continuous everywhere except the set /spl sigma/=/spl sigma//spl dot/=/spl middot//spl middot//spl middot/=/spl sigma//sup (r-1)/=0. A robust output-feedback controller version provides for the tracking accuracy proportional to the sampling noise magnitude.