Stabilization of Asymptotically Time-Invariant Linear Time-Varying Systems

被引：0

作者：

Sun, Yuli ^{[1
]}

Chi, Wei ^{[1
]}

Xiao, Jinmei ^{[1
]}

Yu, Tianqiu ^{[1
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China

来源：

2014 11TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA) | 2014年

关键词：

asymptotically time-invariant systems; stabilization; fredholm operators; coprime factorizations; TOPOLOGICAL STABLE RANK; NEST-ALGEBRAS; OPERATORS;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we study the stabilization problem of asymptotically time-invariant linear time-varying systems within the framework of nest algebras. The main theorem of the paper establishes that an asymptotically time-invariant system is stabilizable if and only if the time-invariant part is also stabilizable. The proof relies on the theory of Fredholm and compact operators. In particular, when the compact part of systems are strictly causal, we show that a controller (possibly time-varying) stabilizes system if and only if it stabilizes the time-invariant part.

引用

页码：3881 / 3885

页数：5

共 15 条

[1] SPECTRAL AND FREDHOLM PROPERTIES OF OPERATORS IN ELEMENTARY NEST-ALGEBRAS [J].

BARNES, BA ;

CLAUSS, JM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (05) :1735-1741

[2] ASYMPTOTIC TOEPLITZ-OPERATORS [J].

BARRIA, J ;

HALMOS, PR .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 273 (02) :621-630

[3]

Davidson K.R., 1988, NEST ALGEBRAS

[4] Topological stable rank of nest algebras [J].

Davidson, Kenneth R. ;

Ji, You Qing .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2009, 98 :652-678

[5] On strong stabilization for linear time-varying systems [J].

Feintuch, A .

SYSTEMS & CONTROL LETTERS, 2005, 54 (11) :1091-1095

[6]

Feintuch A., 1982, SYATEM THEORY HILBER

[7]

Feintuch A., 1998, Robust Control Theory in Hilbert Space

[8] On strong stabilization for linear continuous time time-varying systems [J].

Feintuch, Avraham .

SYSTEMS & CONTROL LETTERS, 2008, 57 (09) :691-695

[9] On strong stabilization of asymptotically time-invariant linear time-varying systems [J].

Feintuch, Avraham .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2011, 22 (03) :229-243

[10]

Gohberg I., 1990, CLASSES LINEAR OPERA, V1

← 1 2 →