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.
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页码：1077 / 1093
页数：17
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