A Refinement of the Generalized Chordal Distance

DOI10.1137/130918095zbMATH Open1307.93131arXiv1304.5911OpenAlexW2964117260MaRDI QIDQ5244630

Amol Sasane

Publication date: 27 March 2015

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Abstract: For single input single output systems, we give a refinement of the generalized chordal metric. Our metric is given in terms of coprime factorizations, but it coincides with the extension of Vinnicombe's nu-metric given in earlier work by Ball and Sasane if the coprime factorizations happens to be normalized. The advantage of the metric introduced in this article is its easy computability (since it relies only on coprime factorizations, and does not require normalized coprime factorizations). We also give concrete formulations of our abstract metric for standard classes of stable transfer functions.

Full work available at URL: https://arxiv.org/abs/1304.5911

zbMATH Keywords

robust control\(\nu\)-metricBanach algebras of holomorphic functions

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Stabilization of systems by feedback (93D15) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Control/observation systems in abstract spaces (93C25)

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