{"paper":{"title":"On Dimension-Varying Control Systems: A Universal State Space Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daizhan Cheng, Feng Liu, Tielong Shen, Xiaoming Hu","submitted_at":"2026-01-21T10:14:22Z","abstract_excerpt":"This paper develops a unified framework for the analysis and design of dimension-varying control systems by constructing an intrinsic quotient state space, $\\Omega$. A significant challenge in non-fixed-dimensional systems is the lack of a common metric space that enables comparison of states across dimensions without relying on arbitrary external embeddings. To address this, we propose a cross-dimensional pseudo-metric $d_{\\mathcal{V}}$ on $\\mathbb{R}^{\\infty}$ and derive $\\Omega$ by identifying zero-distance representatives. We demonstrate that $\\Omega$ preserves the essential topological an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.14839","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.14839/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}