Robust exact finite-time output based control using high-order sliding modes

Linear time-invariant systems with matched perturbations are exactly stabilised in finite time by means of dynamic output-feedback control under the assumptions of a permanent complete vector relative degree and bounded perturbations. The approach makes use of non-homogeneous high-order sliding-mode controllers and differentiators. A criterion of the differentiator convergence is developed for the detection of a proper time of turning on the controller. A gain adaptation strategy is proposed for both controller and differentiator. The performance with noisy discrete sampling is studied.