Contractibility of dynamic LTI controllers using complementary matrices

Author

Bakule, Lubomír ; Rodellar, José ; Rossell, Josep M.

Author_Institution

Inst. of Inf. Theor. & Autom., Acad. of Sci. of the Czech Republic, Prague, Czech Republic

Volume

48

Issue

7

fYear

2003

fDate

7/1/2003 12:00:00 AM

Firstpage

1269

Lastpage

1274

Abstract

A generalized structure of complementary matrices involved in the input-state-output inclusion principle for linear time-invariant systems including contractibility conditions for static state feedback controllers is well known. In this note, it is shown how to further extend this structure when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion/contraction transformation matrices. Explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion/contraction transformation matrices. Moreover, these conditions are further specialized for a particular class of transformation matrices.

Keywords

control system synthesis; linear systems; matrix algebra; state feedback; complementary matrices; contractibility conditions; dynamic LTI controller contractibility; expansion/contraction transformation matrices; input-state-output inclusion principle; linear time-invariant systems; necessary and sufficient conditions; static state feedback controllers; Automation; Control system analysis; Control systems; Distributed control; Information theory; Large-scale systems; Linear feedback control systems; Mathematics; State feedback; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2003.814275

Filename

1211228