Discrete-Time Dichotomous Well-Posed Linear Systems and Generalized Schur-Nevanlinna-Pick Interpolation

被引：17

作者：

Ball, Joseph A. ^{[1
]}

Raney, Michael W. ^{[1
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2007年 / 1卷 / 01期

关键词：

Shift-invariant subspace; dichotomous realization; strongly regular J-inner function; Grassmannian approach to interpolation;

D O I：

10.1007/s11785-006-0001-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a class of matrix-valued functions W called "L-2-regular". In case W is J-inner, this class coincides with the class of "strongly regular J-inner" matrix functions in the sense of Arov-Dym. We show that the class of L-2-regular matrix functions is exactly the class of transfer functions for a discrete-time dichotomous (possibly infinite-dimensional) input-state-output linear system having some additional stability properties. When applied to J-inner matrix functions, we obtain a state-space realization formula for the resolvent matrix associated with a generalized Schur-Nevanlinna-Pick interpolation problem.

引用

页码：1 / 54

页数：54

共 46 条

[1]

Arov DZ, 2005, OPER THEOR, V160, P101

[2]

Arov DZ, 2004, OPER THEOR, V149, P79

[3] Criteria for the strong regularity of J-inner functions and γ-generating matrices [J].