Finite-time stabilization of uncertain SISO systems

Any uncertain smooth single-input single-output dynamic system of the full relative degree can be locally finite-time stabilized at its equilibrium point by means of a standard continuous feedback. High-order sliding-mode approach is modified for this sake, and a list of continuous controllers is built depending only on the given relative degree n of the system output sigma. Provided the relative degree is globally well-defined and the system growth rate is restricted, the global finite-time stabilization is possible. The asymptotic accuracies in the cases of discrete and noisy sampling are estimated. In particular, for any q > 0 the stabilization accuracy sigma ⁽ⁱ⁾ = O (zeta ^n-i+q ), i = 0, 1, ..., n - 1, is obtained, where zeta is the sampling interval, and q is an arbitrarily chosen positive feedback parameter. Output-feedback controllers are constructed. Computer simulation confirms the applicability of the approach.