Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control

• 成果类型: Article
• 署名作者: Lhachemi, Hugo; Prieur, Christophe
• 署名单位: University College Dublin; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2975003
• 发表日期: 2021
• 页码: 105-120
• 关键词: Delays; Mathematical model; control design; Lyapunov methods; Eigenvalues and eigenfunctions; Closed loop systems; Distributed parameter systems; delay boundary control; Lyapunov function; partial differential equation (PDE)-ordinary differential equation (ODE) interconnection

摘要

This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinite-dimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.