DocumentCode
817798
Title
Geometric interpretation of complex vectors arising in the frequency-domain analysis of multivariable systems
Author
Vesty, Paul
Author_Institution
Hawker Siddeley Dynamics Ltd., Hatfield, Herts., England
Volume
20
Issue
1
fYear
1975
fDate
2/1/1975 12:00:00 AM
Firstpage
157
Lastpage
158
Abstract
It is shown that an 
-dimensional vector whose components are complex numbers can be visualized as a plane ellipse in geometric -space. The length and direction of a complex vector are interpreted in terms of the ellipse axes thus giving a deeper insight into the eigenstructure of system transfer matrices. The system characteristic ellipse is introduced and its application to the measurement of characteristic loci is discussed.
-dimensional vector whose components are complex numbers can be visualized as a plane ellipse in geometric -space. The length and direction of a complex vector are interpreted in terms of the ellipse axes thus giving a deeper insight into the eigenstructure of system transfer matrices. The system characteristic ellipse is introduced and its application to the measurement of characteristic loci is discussed.Keywords
Eigenvalues; Linear systems, time-invariant continuous-time; Transfer function matrices; Eigenvalues and eigenfunctions; Equations; Frequency domain analysis; Length measurement; MIMO; Negative feedback; Output feedback; Transforms; Turning; Visualization;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1975.1100872
Filename
1100872
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