BOUNDARY FEEDBACK STABILIZATION FOR AN UNSTABLE TIME FRACTIONAL REACTION DIFFUSION EQUATION

被引：73

作者：

Zhou, Hua-Cheng ^{[1
,2
]}

Guo, Bao-Zhu ^{[3
,4
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China

[2] Tel Aviv Univ, Sch Elect Engn, IL-69978 Ramat Aviv, Israel

[3] Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[4] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 01期

基金：

中国国家自然科学基金; 以色列科学基金会;

关键词：

time fractional reaction diffusion equation; boundary control; output feedback; stabilization; DISTURBANCE REJECTION CONTROL; SLIDING MODE CONTROL; MULTIDIMENSIONAL WAVE-EQUATION; BERNOULLI BEAM EQUATION; ACTIVE DISTURBANCE; APPROXIMATE CONTROLLABILITY; SYSTEMS; SUBJECT;

D O I：

10.1137/15M1048999

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations. New state feedback controls with actuation on one end are designed by the backstepping method for both Dirichlet and Neumann boundary controls. By the Riesz basis approach and the fractional Lyapunov method, we prove the existence and uniqueness and the Mittag-Leffler stability for the closed-loop systems. For both cases, the observers and the observer based output feedback are designed to stabilize the systems.

引用

页码：75 / 101

页数：27

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