Necessary Stability Conditions for Reaction-Diffusion-ODE Systems

• 成果类型: Article
• 署名作者: Bajodek, Mathieu; Lhachemi, Hugo; Valmorbida, Giorgio
• 署名单位: Universite Paris Saclay; Inria; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3407818
• 发表日期: 2024
• 页码: 7940-7947
• 关键词: Numerical stability; Stability criteria; asymptotic stability; vectors; Transfer functions; mathematical models; Boundary conditions; Distributed parameter systems; reaction-diffusion; Semidefinite programming; stability of linear systems

摘要

This article reports necessary stability conditions for a parabolic partial differential equation (PDE) interconnected through the boundaries to an ordinary differential equation (ODE). We intend to propose numerical certificates for the instability of such interconnections. From one side, using spectral methods, we derive a necessary analytical condition based on root locus analysis, which can be tested in the parameters space. On the other side, using Lyapunov direct and converse approaches, two necessary conditions of stability are established in terms of matrix inequalities. The novelties lie both in the type of system studied and in the converse stability methods that are used. The numerical results demonstrate the performance of the different criteria set up in this article.