Discrete differentiators based on sliding modes

Sliding-mode-based differentiation of the input f(t) yields exact estimations of the derivatives ḟ,…,f⁽ⁿ⁾, provided an upper bound L(t) of |f⁽ⁿ⁺¹⁾(t)| is available in real-time. In practice it involves discrete sampling and numerical integration of the internal variables between the measurements. Accuracy asymptotics of different discretization schemes are calculated for discrete noisy sampling, whereas sampling and integration steps are independently variable or constant. Proposed discrete differentiators restore the optimal accuracy asymptotics of their continuous-time counterparts. Event-triggered sampling is considered. Extensive numeric experiments are presented and analyzed.