{"paper":{"title":"Universal regular control for generic semilinear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jairo Bochi, Nicolas Gourmelon","submitted_at":"2012-01-09T00:29:56Z","abstract_excerpt":"We consider discrete-time projective semilinear control systems $\\xi_{t+1} = A(u_t) \\cdot \\xi_t$, where the states $\\xi_t$ are in projective space $\\mathbb{R}P^{d-1}$, inputs $u_t$ are in a manifold $U$ of arbitrary finite dimension, and $A \\colon U \\to GL(d,\\mathbb{R})$ is a differentiable mapping.\n  An input sequence $(u_0,\\ldots,u_{N-1})$ is called universally regular if for any initial state $\\xi_0 \\in \\mathbb{R}P^{d-1}$, the derivative of the time-$N$ state with respect to the inputs is onto.\n  In this paper we deal with the universal regularity of constant input sequences $(u_0, \\dots, u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1672","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"}