Pré-Publication, Document De Travail Année : 2025

LMI results using IQCs and projections for the heat equation coupled to ODEs

Résumé

This paper investigates the stability of a coupled system consisting of a finite-dimensional ordinary differential equation (ODE) and a partial differential equation (PDE), with a focus on incorporating boundary condition derivatives into the stability analysis. Building on a combination of projection methods and Integral Quadratic Constraints (IQCs), we develop a novel approach that generates stability conditions through Linear Matrix Inequalities (LMIs). The IQC framework rigorously accounts for the interconnection structure and dissipation mechanisms at the boundaries, providing a more comprehensive analysis of coupled finite and infinite-dimensional systems while explicitly considering boundary condition dynamics and their impact on stability.

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Dates et versions

hal-05038192 , version 1 (17-04-2025)

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  • HAL Id : hal-05038192 , version 1

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Sara Callegari, Frédéric Gouaisbaut, Dimitri Peaucelle. LMI results using IQCs and projections for the heat equation coupled to ODEs. 2025. ⟨hal-05038192⟩
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