Mathematics > Optimization and Control
[Submitted on 26 Mar 2025
(v1)
, last revised 6 Apr 2025 (this version, v2)]
Title: Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities
Title: Lur'e系统的收缩性分析与控制设计：利普希茨、增量扇形有界和单调非线性
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.
Submission history
From: Ryotaro Shima [view email][v1] Wed, 26 Mar 2025 03:07:49 UTC (1,335 KB)
[v2] Sun, 6 Apr 2025 11:30:03 UTC (1,335 KB)
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.