{"paper":{"title":"Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antoine Chaillet, Antonio Lor\\'ia (LSS), Iecn), Mario Sigalotti (INRIA Lorraine / IECN / MMAS, Yacine Chitour (LSS)","submitted_at":"2007-02-23T10:28:37Z","abstract_excerpt":"Consider the controlled system $dx/dt = Ax + \\alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\\mu,T$ such that, for every $t\\geq 0$, $\\int_t^{t+T}\\alpha(s)ds\\geq \\mu$. In particular, when $\\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\\mu,T$, which globally asymptotically stab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702687","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"}