Uniform Robust Exact Differentiator

This paper presents a new type of differentiator, the Uniform Robust Exact Differentiator (URED). The URED provides, in the absence of noise and for every time signal with bounded second derivative, the exact value of the first derivative. The main feature of the URED is that the convergence time is finite and uniform in the initial conditions, that is, the convergence of the URED is attained after a prescribed time independent of the initial conditions of the algorithm. The URED is obtained by adding higher-degree terms to the Super-Twisting Algorithm (STA), that induce the uniformity property of the URED. Convergence is analyzed via strong Lyapunov functions.