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Oustaloup-Recursive-Approximation for Fractional Order Differentiators

version (1.89 KB) by YangQuan Chen
Oustaloup-Recursive-Approximation for fractional order differentiator.


Updated 04 Aug 2003

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% Filename: ora_foc.m
% Oustaloup-Recursive-Approximation for fractional order differentiator

% Input variables:
% r: the fractional order as in s^r, r is a real number
% N: order of the finite TF approximation for both (num/den)
% (Note: 2N+1 recursive z-p pairs)
% w_L: low frequency limit of the range of the frequency of interest
% w_H: upper freq. limit of the range of the frequency of interest
% Output:
% sys_foc: continuous time transfer function system object (TF)

% Reference
% [1] Oustaloup, A.; Levron, F.; Mathieu, B.; Nanot, F.M.; "Frequency-band
% complex noninteger differentiator: characterization and synthesis".
% EEE Transactions on Circuits and Systems I: Fundamental Theory and
% Applications, I , Volume: 47 Issue: 1, Jan. 2000, Page(s): 25 -39
% [2] D. Xue, Y.Q. Chen and D. Atherton. "Linear feedback control -
% analysis and design with Matlab 6.5". Textbook draft. Chapter 9
% "Fractional order control - An introduction". PDF available upon
% request. Send request email to "".

For more information on FOC, check my FOC web

Cite As

YangQuan Chen (2021). Oustaloup-Recursive-Approximation for Fractional Order Differentiators (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (7)


your function helped me alot


thank you

qi xiang

very well

Pritesh Shah

Very well explain



Wojciech Roman

I am interested any documents of Fractional Calculus, fractional Order Controler, ...

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
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