{"paper":{"title":"Optimal $\\mathcal{H}_{2}$ model approximation based on multiple input/output delays systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NA"],"primary_cat":"cs.SY","authors_text":"C\\'edric Seren, Charles Poussot-Vassal, Igor Pontes Duff","submitted_at":"2015-11-17T02:24:53Z","abstract_excerpt":"In this paper, the $\\mathcal{H}_{2}$ optimal approximation of a $n_{y}\\times{n_{u}}$ transfer function $\\mathbf{G}(s)$ by a finite dimensional system $\\hat{\\mathbf{H}}_{d}(s)$ including input/output delays, is addressed. The underlying $\\mathcal{H}_{2}$ optimality conditions of the approximation problem are firstly derived and established in the case of a poles/residues decomposition. These latter form an extension of the tangential interpolatory conditions, presented in~\\cite{gugercin2008h_2,dooren2007} for the delay-free case, which is the main contribution of this paper. Secondly, a two sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05252","kind":"arxiv","version":1},"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"}