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Stability of Transcendental Fractional Systems i

We investigate the stability of transcendental fractional systems, in which the transfer function of a system is given by a ratio of transcendental polynomials: polynomial-like functions with transcendental branch points on the real-axis. We derive root locus rules such as asymptote angles, centroid, number of branches, and arrival and departure angles to deduce the overall stability properties of such systems under feedback.