Abstract
This paper introduces a closed form discretization method of fractional-order differentiators or integrators. Unlike the continued fraction expansion technique, or the infinite impulse response of second-order IIR-type filters, the proposed technique generalizes the Tustin operator to derive a stable and minimum 1st and 2nd-order discrete-time operators (DTO) that discretize continuous fractional-order differintegral operators. Such DTOs exploits the phase properties of the DTOs over a wide range of the frequency spectrum, which depend only on the order of the continuous operators. Moreover, the closed-form DTOs enable one to identify the stability regions of fractional-order discrete-time systems. The effectiveness of this work is demonstrated via several numerical examples.
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