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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.