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Finite Global $H_{\infty}$ Optimization of the $Q$-Filter Time Constant for Nominal-Response Recovery in SISO Disturbance Observers under Parametric Plant Uncertainty — arXiv:2611.01385

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01385
License (as archived): CC0-1.0
Archived: 2026-11-03T19:07:24.116Z
SHA-256 of the archived text: d2ebf715ee7fe8e2c0d3227c9aaac8c0d26dbb6178e67a8beee5d2eed45d71d5
Stable URL of this page: https://metraipolis.com/documento/dc_a5e4be5000fb

How to cite

Finite Global $H_{\infty}$ Optimization of the $Q$-Filter Time Constant for Nominal-Response Recovery in SISO Disturbance Observers under Parametric Plant Uncertainty — arXiv:2611.01385 — arXiv (en), https://arxiv.org/abs/2611.01385 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a5e4be5000fb (Metraipolis archive dc_a5e4be5000fb, sha256 d2ebf715ee7fe8e2c0d3227c9aaac8c0d26dbb6178e67a8beee5d2eed45d71d5)

BibTeX

@misc{dca5e4be5000fb,
  title = {Finite Global $H_infty$ Optimization of the $Q$-Filter Time Constant for Nominal-Response Recovery in SISO Disturbance Observers under Parametric Plant Uncertainty — arXiv:2611.01385},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01385},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a5e4be5000fb; sha256 d2ebf715ee7fe8e2c0d3227c9aaac8c0d26dbb6178e67a8beee5d2eed45d71d5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01385. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper develops a finite real-algebraic procedure for global H-infinity optimization of the time constant of a fixed-shape Q-filter in a single-input/single-output (SISO) disturbance observer (DOB) under affine parametric plant uncertainty. Robust internal stability defines a possibly disconnected feasible domain, and the objective is the worst-case weighted mismatch between the uncertain DOB reference response and the nominal closed-loop response. A recovery-error factorization preserves affine dependence of the performance numerator and denominator on the same uncertainty vector. Phase lifting and a complex-polynomial Edge theorem reduce the uncertainty box to finitely many polynomial edges, while quadratic dependence of the squared frequency-domain inequality on the edge coordinate permits analytic elimination of that coordinate. The resulting semialgebraic formulation has only the squared frequency as a universally quantified variable. It determines the global infimum, decides whether it is attained, and constructs the complete optimizer set over the full robust-stability domain. A DOB case study with a plant family containing non-minimum-phase members yields a unique optimal time constant of approximately 0.0364075 and a worst-case norm of approximately 2.29975. The optimizer lies strictly inside the first robust-stability component, and every smaller feasible time constant in that component has a larger worst-case norm. Finite algebraic certificates establish robust stability, performance feasibility, and strict global optimality.

Tema degli esploratori: calcolo e infrastrutture (elenco arXiv eess.SY, nuovi lavori del giorno).
Categorie arXiv: Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2611.01385 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:25:37.812Z dalla pagina https://arxiv.org/list/eess.SY/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).