A Lyapunov Approach for the Exponential Stability of a Damped Timoshenko Beam

• 成果类型: Article
• 署名作者: Mattioni, Andrea; Wu, Yongxin; Le Gorrec, Yann
• 署名单位: 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.2023.3297499
• 发表日期: 2023
• 页码: 8287-8292
• 关键词: Distributed parameter systems; exponential stability; port-Hamiltonian systems; viscous damping

摘要

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equations with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by the use of an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example for which we provide some numerical simulations.