控制理论与应用2024，Vol.41Issue(12)：2259-2268,10.DOI:10.7641/CTA.2023.30020
一类具有时变系数的抛物系统的积分输入状态镇定问题
Integral input-to-state stabilization of a class of parabolic systems with time-varying coefficients
摘要
Abstract
For parabolic systems with time-varying coefficients,it remains a challenging problem how to design a boundary feedback control via a time-invariant kernel function for ensuring the stability of the closed-loop system.In this paper,the problem of stabilization of certain class of parabolic systems with space-time-varying coefficients is investigated.Specifically,without applying a Gevrey condition and an event-triggered scheme,a boundary feedback controller is de-signed by using a time invariant kernel function.Meanwhile,in order to characterize the influence of external disturbances on the stability of the system,the stability of the closed-loop system is studied in the framework of input-to-state stability theory(ISS theory).In particular,the L1-ISS of the considered system is established in the spatial L1-norm by using the approximative Lyapunov method and comparison principle for parabolic PDEs with nonlocal boundary conditions.The validity of the controller and the proposed approach are further verified by numerical simulations.关键词
积分输入状态稳定性/反步法/镇定/Lyapunov逼近方法/比较原理/抛物方程/时变系数Key words
integral input-to-state stability/backstepping/stabilization/approximative Lyapunov method/comparison principle/parabolic equation/time-varying coefficient引用本文复制引用
陈巧玲,郑军,朱谷川..一类具有时变系数的抛物系统的积分输入状态镇定问题[J].控制理论与应用,2024,41(12):2259-2268,10.基金项目
国家自然科学基金项目(11901482),加拿大自然科学和工程研究委员会(RGPIN-2024-04709)资助.Supported by the National Natural Science Foundation of China(11901482)and the Natural Sciences and Engineering Research Council of Canada(RGPIN-2024-04709). （11901482）
