Boundary Control for Exponential Stabilization of Nonlinear Distributed Parameter Systems Modeled by PIDEs

IEEE Access

Jianlong Qiu¹  Ancai Zhang¹  Fuad E. Alsaadi¹  Zhenxing Li²  Chengdong Yang³  Tingwen Huang⁴ 

[1] Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, China;M University at Qatar, Doha, Qatar;School of Information Science and Technology, Linyi University, Linyi, China;Science Program, Texas A&x0026;

关键词: Boundary control;    partial integro-differential equation systems;   

DOI  :  10.1109/ACCESS.2018.2867343

来源: DOAJ

【 摘 要 】

This paper studies boundary control for exponential stabilization for a distributed parameter system, modeled by semi-linear parabolic partial integro-differential equations (PIDEs) in a 1-D spatial domain. A boundary controller based on boundary measurement is designed for exponential stabilization of the PIDE system, and it is implemented by controlling and measuring only one endpoint of the 1-D spatial domain. With the Lyapunov direct method and Wirtinger's inequality, a sufficient condition for exponential stabilization of the PIDE system with a given decay rate is investigated. Dealing with a special case of PIDE systems, one lemma called Yang inequality is proposed, and a new less conservative sufficient condition is investigated. An example with two cases is given to show the effectiveness and less conservativeness of the proposed methods by using Yang inequality.

【 授权许可】

Unknown