The Integer-Order Approximation of Fractional-Order Systems in the Loewner Framework

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.