{"paper":{"title":"State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.E. Frazho, M.A. Kaashoek, S. ter Horst","submitted_at":"2014-08-09T19:21:28Z","abstract_excerpt":"For the strictly positive case (the suboptimal case), given stable rational matrix functions $G$ and $K$, the set of all $H^\\infty$ solutions $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\\sup_{|z|\\leq 1}\\|X(z)\\|\\leq 1$, is presented as the range of a linear fractional representation of which the coefficients are presented in state space form. The matrices involved in the realizations are computed from state space realizations of the data functions $G$ and $K$. On the one hand the results are based on the commutant lifting theorem and on the other hand on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2145","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"}