Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence

An universal controller is constructed, formulated in input-output terms only, which causes the output of any uncertain smooth single-input-single-output (SISO) minimum-phase dynamic system with known relative degree to vanish in finite time. That allows exact tracking of arbitrary real-time smooth signals. Only one parameter is to be adjusted. The approach being based on higher-order finite-time-convergence sliding modes, the control can be made arbitrarily smooth, providing for the arbitrarily-high tracking-accuracy order with respect to the sampling step.