Pith Number

pith:5D7DIMUH

pith:2026:5D7DIMUHMPKC6VIFRTGFN6H32S

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Robust $\mathcal{H}_\infty$ Observer Design via Finsler's Lemma and IQCs

Felix Biert\"umpfel, Raktim Bhattacharya

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.

arxiv:2604.03989 v3 · 2026-04-05 · math.OC · cs.SY · eess.SY

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T03:04:40.872350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8fe34328763d42f55058ccc56f8fbd4bbf3b8bef1ba870086047a26f500d8fa

Aliases

arxiv: 2604.03989 · arxiv_version: 2604.03989v3 · doi: 10.48550/arxiv.2604.03989 · pith_short_12: 5D7DIMUHMPKC · pith_short_16: 5D7DIMUHMPKC6VIF · pith_short_8: 5D7DIMUH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5D7DIMUHMPKC6VIFRTGFN6H32S \
  | 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: e8fe34328763d42f55058ccc56f8fbd4bbf3b8bef1ba870086047a26f500d8fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09f56c5222777e932d49e304ef565ad6410753f988fd38bfe20ffd883f285eac",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-05T06:16:15Z",
    "title_canon_sha256": "cd73b9d49200b002d3c6f00655a104afe132bd12f07f07d13734b7e20b8f1fdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03989",
    "kind": "arxiv",
    "version": 3
  }
}