A method for the integer-order approximation of fractional-order systems

A procedure for approximating fractional-order systems by means of integer-order state-space models is presented. It is based on the rational approximation of fractional-order operators suggested by Oustaloup. First, a matrix differential equation is obtained from the original fractional-order representation. Then, this equation is realized in a state-space form that has a sparse block-companion structure. The dimension of the resulting integer-order model can be reduced using an efficient algorithm for rational L2 approximation. Two numerical examples are worked out to show the performance of the suggested technique.