% Step response invariant discretization of fractional order integrators
% srid_fod function is prepared to compute a discrete-time finite dimensional
% (z) transfer function to approximate a continuous-time fractional order
% integrator/differentiator function s^r, where "s" is the Laplace transform variable, and "r" is a
% real number in the range of (-1,1). s^r is called a fractional order
% differentiator if 0 < r < 1 and a fractional order integrator if -1 < r < 0.
% The proposed approximation keeps the step response "invariant"
% r: the fractional order
% Ts: the sampling period
% norder: the finite order of the approximate z-transfer function
% (the orders of denominator and numerator z-polynomial are the same)
% sr: returns the LTI object that approximates the s^r in the sense
% of step response.
% TEST CODE
% Reference: YangQuan Chen. "Impulse-invariant and step-invariant
% discretization of fractional order integrators and differentiators".
% August 2008. CSOIS AFC (Applied Fractional Calculus) Seminar.
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