On the Symmetric Distribution of Interlaced Zero-Pole Pairs approximating the Discrete Fractional Tustin Operator

Abstract

This paper proposes a two steps indirect approach to obtain rational transfer functions (TFs) for implementing the fractional-order Tustin operator (FTO). The coefficients of the rational discrete TF approximation of the FTO are given by closed-form expressions. The proposed coefficients expressions are the basis for proving the zero-pole interlacing of the discrete FTO. The interlaced zero-pole pattern shows a symmetrical configuration on the z-plane.