Singular systems: A new approach in the time domain

Author

Zhou, Zheng ; Shayman, Mark A. ; Tarn, Tzhy-Jong

Author_Institution

Beijing Institute of Information and Control, Beijing, China

Volume

32

Issue

1

fYear

1987

fDate

1/1/1987 12:00:00 AM

Firstpage

42

Lastpage

50

Abstract

A new approach in the time domain is developed for the study of singular linear systems of the form $E\\dot{x} = Ax + Bu, y = Cx$ with $E$ singular. Central to the approach is the fundamental triple $((\\alpha E - A)^{-1}E, (\\alpha E - A)^{-1}B, C)$ with α a real number satisfying det $(\\alpha E - A) \\neq 0$ . Controllability and observability matrices are expressed in terms of the fundamental triple. New tests for impulse controllability and impulse observability are also established. Feedback control problems including pole placement, decoupling, and disturbance localization are studied by use of a modified proportional and derivative feedback of the state in the form of $u = F(\\alpha x - \\dot{x})+ v$ .

Keywords

Linear systems; Singular systems; State-feedback, linear systems; Transient analysis; Circuits; Control theory; Controllability; Feedback control; Frequency; Impulse testing; Large-scale systems; Linear systems; Observability; State feedback;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1987.1104430

Filename

1104430