{"paper":{"title":"Linearizations for Rosenbrock system polynomials and rational matrix functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Namita Behera, Rafikul Alam","submitted_at":"2015-05-14T07:01:16Z","abstract_excerpt":"Our aim in this paper is two-fold: First, for computing zeros of a linear time-invariant (LTI) system $\\Sigma$ in {\\em state-space form}, we introduce a \"trimmed structured linearization\", which we refer to as {\\em Rosenbrock linearization}, of the Rosenbrock system polynomial $\\mathcal{S}(\\lam)$ associated with $\\Sigma.$ We also introduce Fiedler-like matrices for $\\mathcal{S}(\\lam)$ and describe constructions of Fiedler-like pencils for $\\mathcal{S}(\\lam).$ We show that the Fiedler-like pencils of $\\mathcal{S}(\\lam)$ are Rosenbrock linearizations of the system polynomial $\\mathcal{S}(\\lam).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03636","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"}