{"paper":{"title":"A Note on Overshoot Estimation in Pole Placements","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"D. Cheng, L. Guo, Y. Lin, Y. Wang","submitted_at":"2005-09-29T20:11:44Z","abstract_excerpt":"In this note we show that for any given controllable pair (A,B) and any c> 1, a gain matrix K can be chosen so that the transition matrix of the system x' = (A+BK)x decays at the exponential rate exp(-ct) and the overshoot of the transition matrix can be bounded by Mc^L for some M and L that are independent of the choice of c."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509705","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"}