A semigroup characterization of well-posed linear control systems

被引：5

作者：

Bombieri, Miriam ^{[1
]}

Engel, Klaus-Jochen ^{[2
]}

机构：

[1] Math Inst, Arbeitsbereich Funkt Anal, D-72076 Tubingen, Germany

[2] Univ Aquila, Dipartimento Ingn & Sci Informaz Matemat, I-67100 Laquila, Italy

来源：

SEMIGROUP FORUM | 2014年 / 88卷 / 02期

关键词：

Well-posed linear systems; Admissible control operator; Admissible output operator; Laplace transform; Fourier multiplier; Lax-Phillips semigroup; ADMISSIBLE OBSERVATION OPERATORS; CARLESON MEASURE CRITERION; DIAGONAL SEMIGROUPS; UNBOUNDED CONTROL; INPUT ELEMENTS; HILBERT-SPACE; STATE; L2;

D O I：

10.1007/s00233-013-9545-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the well-posedness of a linear control system I (A pound,B,C,D) with unbounded control and observation operators. To this end we associate to our system an operator matrix on a product space and call it p-well-posed if generates a strongly continuous semigroup on . Our approach is based on the Laplace transform and Fourier multipliers. The results generalize and complement those of Curtain and Weiss (Int. Ser. Numer. Math. vol. 91. Birkhauser, Basel, 1989), Staffans and Weiss (Trans. Am. Math. Soc. 354:3229-3262, 2002) and are illustrated by a heat equation with boundary control and point observation.

引用

页码：366 / 396

页数：31

共 50 条

[1] A semigroup characterization of well-posed linear control systems
Miriam Bombieri
Klaus-Jochen Engel
[J]. Semigroup Forum, 2014, 88 : 366 - 396
[2] Quadratic optimal control of well-posed linear systems
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[3] Quadratic optimal control of well-posed linear systems
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