Homogeneous High-Order Sliding Modes

Homogeneity of dynamic systems provides for a number of practically important features. In particular, the finite-time convergence is easily proved, and the asymptotic accuracy is readily calculated in the presence of input noises, delays and discrete sampling. General uncertain single-input-single-output regulation problems are only solvable by means of discontinuous control via the so-called high-order sliding modes (HOSM). Robust output-feedback homogeneous HOSM controllers are produced, using robust exact homogeneous differentiators. The dangerous chattering effect is removed in a standard way. The system performance is not sensitive to the presence of unaccounted-for fast stable dynamics of actuators and sensors, delays and discrete sampling.