On the rational approximation of fractional order systems

Abstract

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.