Exact Differentiation of Signals with Unbounded Higher Derivatives

The proposed arbitrary-order differentiator based on high-order sliding modes is generalized to ensure exact robust nth-order differentiation of signals with a given functional bound of the (n + 1)th derivative. The asymptotic accuracies in the presence of noises and discrete sampling are estimated. The results are applicable for the global observation of system states when the dynamics is unbounded. Computer simulation confirms the applicability of the differentiator

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