{"paper":{"title":"Extension of the $\\nu$-metric for stabilizable plants over $H^\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.AP","math.FA","math.RA"],"primary_cat":"math.OC","authors_text":"Amol Sasane","submitted_at":"2011-07-29T10:58:03Z","abstract_excerpt":"An abstract $\\nu$-metric was introduced by Ball and Sasane, with a view towards extending the classical $\\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. In this short note, we give an important concrete special instance of the abstract $\\nu$-metric, by verifying that all the assumptions demanded in the abstract set-up are satisfied when the ring of stable transfer functions is the Hardy algebra $H^\\infty$. This settles the open question implicit in \\cite{BalSas2}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5928","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}