DocumentCode
851118
Title
The proof of Goka´s conjecture
Author
Yuqiu, Zhao
Author_Institution
Sun-Yat Sen University, Guang Zhou, China
Volume
31
Issue
10
fYear
1986
fDate
10/1/1986 12:00:00 AM
Firstpage
972
Lastpage
974
Abstract
If the system 
is controllable with 
for all 
, then the eigenvalues of 
lie on the unit circle. This is Goka\´s conjecture. Through algebraic transformation and discussion of invariant proper subsets, this note gives a proof of the conjecture, and shows that for more general discrete-time bilinear systems, the conjecture is still true.
is controllable with for all , then the eigenvalues of lie on the unit circle. This is Goka\´s conjecture. Through algebraic transformation and discussion of invariant proper subsets, this note gives a proof of the conjecture, and shows that for more general discrete-time bilinear systems, the conjecture is still true.Keywords
Bilinear systems; Controllability, nonlinear systems; Discrete-time systems; Eigenvalues/eigenvectors; Circuit stability; Control nonlinearities; Control systems; Eigenvalues and eigenfunctions; Frequency dependence; Integral equations; Lyapunov method; Nonlinear control systems; Power system analysis computing; Power system stability;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1986.1104150
Filename
1104150
Link To Document