A revised look at numerical differentiation with an application to nonlinear feedback control

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

“…The objective is to estimate the n th order derivative of x using x ̟ . For this purpose, we apply a class of algebraic differentiators involving Jacobi polynomials, which were introduced in [7,8] using a recent algebraic parametric method (see [13] for other algebraic differentiators).…”

“…Different from the existing polynomial approaches, the idea of the Jacobi differentiator is to use a sliding integration window to estimate the value of x (n) at each t 0 ∈ I by D (n) κ,µ,T,q x(t 0 − T ξ) with a fixed value of ξ ∈ [0, 1] (see [7,8]). If ξ = 0, then it produces a delay of value T ξ.…”

“…[3][4][5][6][7][8][9][10][11][12][13]). The obtained so-called algebraic differentiators are divided into two classes: model-based differentiators and model-free differentiators.…”

“…The first model-free differentiator was introduced in [6] by applying the algebraic method to the truncated Taylor series expansion of the signal to differentiate. Then, two model-free differentiators were studied in [7,8], where the so-called Jacobi differentiator is the most used. Moreover, it was shown that the Jacobi differentiator can also be obtained by taking the truncated Jacobi orthogonal series expansion of the signal to differentiate.…”

“…Moreover, it was shown that the Jacobi differentiator can also be obtained by taking the truncated Jacobi orthogonal series expansion of the signal to differentiate. Then, it was significantly improved by admitting a time-delay [7,8].…”