Existence of stable Lur'e systems for which the O'Shea-Zames-Falb stability test fails

Andrey Kharitenko

Existence of stable Lur'e systems for which the O'Shea-Zames-Falb stability test fails

Optimization and Control 2026-07-26 v1

Authors: Andrey Kharitenko

Abstract

In this note we show that the well-known stability test proposed by O'Shea, Zames and Falb is not necessary for robust stability of Lur'e systems with slope-restricted nonlinearities and thereby disprove a conjecture by J. Carrasco. Specifically we construct a full-block multiplier which certifies stability of a constructed Lur'e interconnection that does not admit an OZF multiplier.

Keywords

Lur'e systems stability test O'Shea-Zames-Falb multiplier slope-restricted nonlinearities robust stability counterexample

Cite

@article{arxiv.2607.23599,
  title  = {Existence of stable Lur'e systems for which the O'Shea-Zames-Falb stability test fails},
  author = {Andrey Kharitenko},
  journal= {arXiv preprint arXiv:2607.23599},
  year   = {2026}
}

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12 pages