Lyapunov Functions for Continuous and Discontinuous Differentiators

Abstract

Given a (differentiable) signal it is an important task for many applications to estimate on line its derivatives. Some well known algorithms to solve this problem include the (continuous) high-gain observers and (discontinuous) Levant’s exact differentiators. In this work we present a family of homogeneous differentiators, encompassing these two algorithms, and we propose a unified smooth Lyapunov function, that allows a common framework to study their convergence and performance analysis.