A Method for the Hankel-Norm Approximation of Fractional-Order Systems

A model-reduction methodology for fractional-order systems based on the Hankel-norm is presented. The methodology involves the truncation of a Laurent series associated with the fractional-order system in a transformed domain. The truncated Laurent series coefficients are used to construct a finite-order transfer function to approximate the original system. Standard model-reduction techniques are then applied to obtain a final low-order approximation. The Hankel norm of the approximation error can be specified a priori. The approximation method is applied to several fractional-order and other infinite-order systems. It is shown to be more generally applicable than standard finite-order modeling techniques.