WELL-POSEDNESS AND REGULARITY OF HYPERBOLIC BOUNDARY CONTROL SYSTEMS ON A ONE-DIMENSIONAL SPATIAL DOMAIN

被引：57

作者：

Zwart, Hans ^{[1
]}

Le Gorrec, Yann ^{[2
]}

Maschke, Bernhard ^{[3
]}

Villegas, Javier ^{[4
]}

机构：

[1] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

[2] FEMTO ST AS2M, F-25000 Besancon, France

[3] Univ Lyon 1, CPE Lyon, CNRS, LAGEP,UMR 5007, F-69622 Villeurbanne, France

[4] AVL Powertrain UK, Basildon SS15 6SR, England

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2010年 / 16卷 / 04期

关键词：

Infinite-dimensional systems; hyperbolic boundary control systems; C-0-semigroup; well-posedness; regularity; DIRICHLET CONTROL; WAVE-EQUATION; BEAM;

D O I：

10.1051/cocv/2009036

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C-0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

引用

页码：1077 / 1093

页数：17

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