Pith Number

pith:XOVZJXTJ

pith:2025:XOVZJXTJDN6OEEVNHMC2GHIMI2

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Coefficient-level output-feedback stabilization of linear port-Hamiltonian descriptor systems

Juan Zhang, Shuo Shi

Coefficient-level conditions stabilize linear port-Hamiltonian descriptor systems via output feedback without explicit representation.

arxiv:2512.23203 v2 · 2025-12-29 · math.OC

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Claims

C1strongest claim

For proportional output feedback, we derive coefficient-level conditions that are equivalent to the known solvability criteria in the explicit pH setting. These conditions ensure that the closed-loop system is regular, impulse-free, asymptotically stable, and remains port-Hamiltonian.

C2weakest assumption

A port-Hamiltonian representation is known to exist for the given coefficient matrices but is not explicitly computed; the coefficient-level conditions are assumed to be checkable directly from the matrices without that representation.

C3one line summary

Coefficient-level conditions are given for proportional and proportional-derivative output feedback that render linear pH descriptor systems regular, impulse-free, asymptotically stable, and port-Hamiltonian without explicit pH forms.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] [1]C. Beattie, V. Mehrmann, and H. Xu,Port-Hamiltonian realizations of linear time invariant systems, arXiv preprint, https://arxiv.org/abs/2201.05355, (2022). [2]C. Beattie, V. Mehrmann, H. Xu, and H 2022 · doi:10.1137/s0363012994272630

[2] [21]J. Kautsky, N. Nichols, and E.-W. Chu,Robust pole assignment in singular control sys- tems, Linear Algebra Appl., 121 (1989), pp. 9–37, https://doi.org/10.1016/0024-3795(89) 90689-7. [22]P. Kunkel 1989 · doi:10.1016/0024-3795(89

[3] [23]C. Mehl, V. Mehrmann, and M. Wojtylak,Linear algebra properties of dissipative Hamil- tonian descriptor systems, SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1489–1519, https://doi.org/10.1137/18M11 2018 · doi:10.1137/18m1164275

[4] [30]M. Shayman and Z. Zhou,Feedback control and classification of generalized linear systems, IEEE Trans. Automat. Control, 32 (1987), pp. 483–494, https://doi.org/10.1109/TAC. 1987.1104642. [31]V. L. 1987 · doi:10.1109/tac

[5] [35]T. Xu, Y. Zeng, L. Zhang, and J. Qian,Direct modeling method of generalized Hamiltonian system and simulation simplified, Procedia Eng., 31 (2012), pp. 901–908, https://doi.org/ 10.1016/j.proeng.2 2012 · doi:10.1016/j.proeng.2012.01.1119

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Receipt and verification

First computed	2026-05-17T23:39:04.545435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbab94de691b7ce212ad3b05a31d0c4680b6b6c6846d2a7e30c6fd8b00867517

Aliases

arxiv: 2512.23203 · arxiv_version: 2512.23203v2 · doi: 10.48550/arxiv.2512.23203 · pith_short_12: XOVZJXTJDN6O · pith_short_16: XOVZJXTJDN6OEEVN · pith_short_8: XOVZJXTJ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/XOVZJXTJDN6OEEVNHMC2GHIMI2 \
  | 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: bbab94de691b7ce212ad3b05a31d0c4680b6b6c6846d2a7e30c6fd8b00867517

Canonical record JSON

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    "primary_cat": "math.OC",
    "submitted_at": "2025-12-29T04:58:03Z",
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