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.