On discretization of high-order sliding modes

Output-feedback high-order sliding-mode (HOSM) controls include HOSM-based differentiators and, therefore, possess complicated discontinuous dynamics. Their practical application naturally involves discrete noisy output sampling and numeric integration of the internal variables. Resulting hybrid systems are shown to be stable, and the corresponding asymptotic sliding-mode accuracies are calculated in the presence of Euler integration and discrete sampling, whereas both might feature variable or constant time steps. Discrete differentiators are developed which restore the optimal accuracy of their continuous-time counterparts. Numeric criteria detect the end of the differentiator transient. Simulation confirms the presented results.