The Integer–Order Approximation of Fractional–Order Systems in The Loewner Framework

Abstract

Abstract This paper deals with the integer–order (finite–dimensional) approximation of a fractional–order (infinite–dimensional) system using the interpolation approach in the Loewner framework. First given a set of interpolation frequencies and the corresponding values of the original noninteger–order transfer function, a Loewner matrix and a shifted Loewner matrix are created. Then, from these matrices an integer–order model in state–space descriptor form is constructed. Its transfer function matches the original system transfer function at the given frequencies. To avoid singularity problems related to data redundancy, a truncated singular value decomposition may finally be applied. Numerical simulations show that the suggested approach to fractional–order system approximation compares favourably with alternative techniques recently presented in the literature to the same purpose.