Integral input-to-state stabilization of a class of parabolic systems with time-varying coefficients

被引：0

作者：

Chen, Qiao-Ling ^{[1
]}

Zheng, Jun ^{[1
,2
]}

Zhu, Gu-Chuan ^{[2
]}

机构：

[1] School of Mathematics, Southwest Jiaotong University, Sichuan, Chengdu

[2] Department of Electrical Engineering, Polytechnique Montréal, Montreal, H3T 1J4, QC

来源：

Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2024年 / 41卷 / 12期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

approximative Lyapunov method; backstepping; comparison principle; integral input-to-state stability; parabolic equation; stabilization; time-varying coefficient;

D O I：

10.7641/CTA.2023.30020

中图分类号：

学科分类号：

摘要：

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 designed 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. © 2024 South China University of Technology. All rights reserved.

引用

页码：2259 / 2268

页数：9

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