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 :
