Synthesis on a class of algebraic differentiators and application to nonlinear observation

The recent algebraic parametric method proposed by Fliess and Sira-Ramírez [1, 2] has been extended to numerical differentiation problem in noisy environment. The obtained algebraic differentiators are non-asymptotic and robust against corrupting noises. Among these algebraic differentiators, the Jacobi differentiator has been used in many applications (see, e.g. [15-17]). In this paper, we summarize some existing error analysis results to give a strategy on how to chose the design parameters for the Jacobi differentiator. Then, we provide new algorithms which are more robust against the numerical errors produced by negative design parameters´ values. Finally, we consider an application to nonlinear observation, where we compare the Jacobi differentiator to the high gain observer and the high order sliding modes differentiator.