Finite-dimensional controller design for semilinear parabolic systems

被引：2

作者：

Yan, Y. ^{[1
]}

Coca, D. ^{[1
]}

Barbu, V. ^{[2
]}

机构：

[1] Univ Sheffield, Dept Automat Control & Syst Engn, Sheffield S1 3JD, S Yorkshire, England

[2] Alexandru Ioan Cuza Univ, Dept Math, Iasi 700506, Romania

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 12期

基金：

英国工程与自然科学研究理事会;

关键词：

Parabolic system; Feedback controller; Riccati equation; Finite element method; INTERNAL STABILIZATION;

D O I：

10.1016/j.na.2008.10.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers the stabilization of steady-state Solutions of a semilinear parabolic system using finite-dimensional feedback controllers with support in an arbitrary open subset and which are active in one equation only. It is shown that such a controller, with dimension given by the largest algebraic multiplicity of the unstable eigenvalues of the linearized system, exponentially stabilizes the steady-state Solution. An optimal design methodology for these types of controllers, which is based oil the finite element approximation of the semilinear parabolic system, is introduced and illustrated by numerical simulation examples. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：4451 / 4475

页数：25

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