Pith Number

pith:T7LLG5YG

pith:2026:T7LLG5YG4FQK7XN6PIQE5TERQC

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Characterization of stability radii for robustly asymptotically stable dissipative Hamiltonian differential-algebraic systems

Anshul Prajapati, Peter Benner, Punit Sharma, Volker Mehrmann

Dissipative Hamiltonian differential-algebraic systems remain robustly asymptotically stable exactly when the smallest structure-preserving perturbation that destroys stability has positive size.

arxiv:2605.13891 v1 · 2026-05-12 · math.DS · cs.NA · math.NA · math.OC

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Claims

C1strongest 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.

C2weakest assumption

The systems under study are linear time-invariant dissipative Hamiltonian differential-algebraic systems, with perturbations required to preserve the Hamiltonian structure.

C3one line summary

Exact conditions and bounds are derived for when robust asymptotic stability is lost in dissipative Hamiltonian DAEs under structure-preserving perturbations.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] 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 2021

[2] 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 2020

[3] 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 2021

[4] 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 2021

[5] 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 2018

Receipt and verification

First computed	2026-05-17T23:39:19.054109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fd6b37706e160afddbe7a204ecc9180b972ee4fca61f74021a534d345141831

Aliases

arxiv: 2605.13891 · arxiv_version: 2605.13891v1 · doi: 10.48550/arxiv.2605.13891 · pith_short_12: T7LLG5YG4FQK · pith_short_16: T7LLG5YG4FQK7XN6 · pith_short_8: T7LLG5YG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T7LLG5YG4FQK7XN6PIQE5TERQC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9fd6b37706e160afddbe7a204ecc9180b972ee4fca61f74021a534d345141831

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5406a808b39fc507d62bdcb0ec93d44f6d2d6d963bab48af08bb7933cdedcf64",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-12T06:41:30Z",
    "title_canon_sha256": "56c74e915a8def0063758633f332b093b8f4b1cb90a076462c3b5c7443891270"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13891",
    "kind": "arxiv",
    "version": 1
  }
}