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

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.