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
Link To Document :
