Globally convergent fast exact differentiator with variable gains

A new modification of the popular finite-time-convergent robust exact sliding-mode-based differentiator is proposed. Such nth-order differentiator provides for the fast global convergence of its outputs to the first n exact derivatives of its input, provided a time-variable local Lipschitz constant of the input´s nth derivative is available and has a bounded logarithmic derivative. It features the standard asymptotic accuracy of the homogeneous differentiator in the presence of noises and discrete-time sampling. Special discretization preserves the same accuracy, when the differentiator is realized as a discrete-time system.