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arXiv · 2503.20177

Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities

Ryotaro Shima·Alexander Davydov·Francesco Bullo
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Abstract

In this paper, we study the contractivity of Lur'e dynamical systems whose nonlinearity is either Lipschitz, incrementally sector bounded, or monotone. We consider both the discrete- and continuous-time settings. In each case, we provide state-independent linear matrix inequalities (LMIs) which are necessary and sufficient for contractivity. Additionally, we provide LMIs for the design of controller gains such that the closed-loop system is contracting. Finally, we provide a numerical example for control design.

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Ryotaro Shima, Alexander Davydov, Francesco Bullo. 2025-03-26. Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities. https://arxiv.org/abs/2503.20177

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