Abstract
Abstract A simple presentation and derivation of the robustness properties of single-input single-output feedback systems with rational transfer functions are given. Frequency response plots in the complex plane are stereographically projected onto the Riemann sphere. Here we adopt the chordal distance between two such projections as the distance between the two systems. A metric is thus obtained for approximating stable and unstable systems. This chordal metric is the basis of the proposed study of robustness. Several results in parallel with those obtained by Zames and El-Sakkary (1980) are developed using elementary geometric properties of the plane and the sphere.
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