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Root distribution of delta-operator formulated polynomials

Root distribution of delta-operator formulated polynomials

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Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden–Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden–Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

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