{"paper":{"title":"Characterization of stability radii for robustly asymptotically stable dissipative Hamiltonian differential-algebraic systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Dissipative Hamiltonian differential-algebraic systems remain robustly asymptotically stable exactly when the smallest structure-preserving perturbation that destroys stability has positive size.","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"math.DS","authors_text":"Anshul Prajapati, Peter Benner, Punit Sharma, Volker Mehrmann","submitted_at":"2026-05-12T06:41:30Z","abstract_excerpt":"We study linear time-invariant dissipative Hamiltonian differential-algebraic systems.\n  We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under structure-preserving perturbations."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under structure-preserving perturbations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The systems under study are linear time-invariant dissipative Hamiltonian differential-algebraic systems, with perturbations required to preserve the Hamiltonian structure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact conditions and bounds are derived for when robust asymptotic stability is lost in dissipative Hamiltonian DAEs under structure-preserving perturbations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Dissipative Hamiltonian differential-algebraic systems remain robustly asymptotically stable exactly when the smallest structure-preserving perturbation that destroys stability has positive size.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"432f43f9485f2d20971daa51758b211918c81e093a0f4f7b85b0019863bacb97"},"source":{"id":"2605.13891","kind":"arxiv","version":1},"verdict":{"id":"0344a7d6-fa63-4771-82f2-5978f4f25e3a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:44:41.091011Z","strongest_claim":"We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under structure-preserving perturbations.","one_line_summary":"Exact conditions and bounds are derived for when robust asymptotic stability is lost in dissipative Hamiltonian DAEs under structure-preserving perturbations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The systems under study are linear time-invariant dissipative Hamiltonian differential-algebraic systems, with perturbations required to preserve the Hamiltonian structure.","pith_extraction_headline":"Dissipative Hamiltonian differential-algebraic systems remain robustly asymptotically stable exactly when the smallest structure-preserving perturbation that destroys stability has positive size."},"references":{"count":38,"sample":[{"doi":"","year":2021,"title":"F. Achleitner, A. Arnold, and V. Mehrmann. Hypocoercivity and controllability in linear semi- dissipative ODEs and DAEs.ZAMM — Zeitschrift f¨ ur Angewandte Mathematik und Mechanik, 103:e202100171, 202","work_id":"39a209cc-4964-4b36-bf84-ec861c9d1e93","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"N. Aliyev, V. Mehrmann, and E. Mengi. Approximation of stability radii for large-scale dissipative Hamiltonian systems.Advances in Computational Mathematics, 46(1):6, 2020","work_id":"cd34d91e-eda2-43b3-af99-0c1cdc435d20","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"R. Altmann, V. Mehrmann, and B. Unger. Port-Hamiltonian formulations of poroelastic network models.Mathematical and Computer Modelling of Dynamical Systems, 27:429–452, 2021","work_id":"0bea83f2-f6b9-4032-a46a-fe11ab12d676","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"M. K. Baghel, N. Gillis, and P. Sharma. Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems.Numerical Linear Algebra with Application","work_id":"f6117d4a-5e74-4065-a9e3-2feea5d4aca9","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"C. Beattie, V. Mehrmann, H. Xu, and H. Zwart. Linear port-Hamiltonian descriptor systems.Math- ematics of Control Signals and Systems, 30(4):17, 2018","work_id":"2d36921e-be3e-479d-89c4-7837ed5424e0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":38,"snapshot_sha256":"65b58d3eb4bad6eb55d28fbd77f41428e5048f0a8500da7deb5c4f57c682fe5e","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"}