{"paper":{"title":"Robust $\\mathcal{H}_\\infty$ Observer Design via Finsler's Lemma and IQCs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A slack variable via Finsler's lemma relaxes the LMI for robust H∞ observer design with IQCs, removing the strict stability requirement and multiplier trade-off.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Felix Biert\\\"umpfel, Raktim Bhattacharya","submitted_at":"2026-04-05T06:16:15Z","abstract_excerpt":"This paper develops a Finsler-based LMI for robust $\\mathcal{H}_\\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement $\\mathrm{He}(PA) \\prec 0$ (which fails for marginally stable dynamics), and a multiplier--Lyapunov trade-off that causes infeasibility for wide uncertainty ranges. For marginally stable dynamics, artifi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement He(PA) ≺ 0 (which fails for marginally stable dynamics), and a multiplier–Lyapunov trade-off that causes infeasibility for wide uncertainty ranges.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That adding artificial damping to the design model for marginally stable dynamics produces an observer whose certified performance remains meaningful for the actual undamped system; this assumption is stated in the abstract but its quantitative effect on the final error bounds is not detailed here.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Finsler-based LMI with slack variables relaxes Lyapunov-IQC coupling to enable robust H∞ observer design for block-structured uncertainty and marginally stable dynamics via artificial damping.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A slack variable via Finsler's lemma relaxes the LMI for robust H∞ observer design with IQCs, removing the strict stability requirement and multiplier trade-off.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a69ee89f7417a8a8eb86ceb116a72d7c4990bdcdb16879f27c8701cba792940f"},"source":{"id":"2604.03989","kind":"arxiv","version":3},"verdict":{"id":"597c2078-27bd-4dc3-a5bb-46e3e0e24298","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T17:28:59.217556Z","strongest_claim":"By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement He(PA) ≺ 0 (which fails for marginally stable dynamics), and a multiplier–Lyapunov trade-off that causes infeasibility for wide uncertainty ranges.","one_line_summary":"A Finsler-based LMI with slack variables relaxes Lyapunov-IQC coupling to enable robust H∞ observer design for block-structured uncertainty and marginally stable dynamics via artificial damping.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That adding artificial damping to the design model for marginally stable dynamics produces an observer whose certified performance remains meaningful for the actual undamped system; this assumption is stated in the abstract but its quantitative effect on the final error bounds is not detailed here.","pith_extraction_headline":"A slack variable via Finsler's lemma relaxes the LMI for robust H∞ observer design with IQCs, removing the strict stability requirement and multiplier trade-off."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.03989/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":2,"snapshot_sha256":"b94586d6bee8e210e1d432c7c6961e4d74aedfc615f56ff521ae927a7ed7800a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}