Robust Exact Fixed-Time Differentiators with Filtering Capabilities

In this paper, a new family of fixed-time differentiators with filtering capabilities is proposed, where each differentiator is capable of both rejecting large noises and exactly differentiating smooth signals. The presented differentiator provides global finite-time convergence of its outputs to the first n<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> exact derivatives of the input signal independently of the initial condition, i.e. the estimations converge in Fixed-Time. Estimation accuracy asymptotics are studied in the presence of noises. Extensive simulations confirm the presented theoretical results.