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Carrasco's Conjecture on the O'Shea-Zames-Falb Test

Differential equations · posed by Joaquin Carrasco · disproved

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Statement

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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Andrey Kharitenko, using ChatGPT 5.5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    A finite-horizon counterexample provided by ChatGPT 5.5 motivated the construction; the author built and certified the full interconnection.

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