Sliding-Mode-Based Differentiation and Filtering

The proposed <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>th-order filter is based on sliding modes (SMs). It exactly estimates <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> input derivatives in the absence of noises, and is robust to noises of small magnitudes or having small average values. Estimation accuracy asymptotics are calculated. The filter is applied to the real-time accurate estimation of the equivalent control in SM control systems.

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