Carrasco's Conjecture on the O'Shea-Zames-Falb Test
Is the O'Shea-Zames-Falb multiplier test necessary for robust stability of Lur'e systems with slope-restricted nonlinearities, as conjectured by Carrasco? No: there is a stable Lur'e interconnection, certified by a full-block multiplier, that admits no OZF multiplier.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Control theory
- Posed by
- Joaquin Carrasco
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-26
- Model
- ChatGPT 5.5
- Vendor
- OpenAI
- Collaborators
- Andrey Kharitenko
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
A finite-horizon counterexample provided by ChatGPT 5.5 motivated the construction; the author built and certified the full interconnection.
Verification
Single-author arXiv note; not yet peer-reviewed.