On the rational approximation of fractional order systems

This paper is concerned with the finite-dimensional approximation of a fractional-order system represented in state-space form. To this purpose, resort is made to the Oustaloup method for approximating a fractional-order integrator by a rational filter. By applying this method to the RHS of the state equation of the fractional-order system, a matrix differential equation is obtained. This equation is then realized in a state-space form whose state matrix exhibits a (sparse) block-companion structure. To reduce the dimension of this integer-order model, an efficient method for L₂ approximation can profitably be applied. Numerical simulations show that the suggested approach compares favourably with alternative techniques recently presented in the literature to the same purpose.