DocumentCode :
827804
Title :
Shift Walsh matrix and delay-differential equations
Author :
Chen, Wen-Liang ; Shih, Yen-ping
Author_Institution :
National Tsing Hua University, Hsinchu, Taiwan
Volume :
23
Issue :
6
fYear :
1978
fDate :
12/1/1978 12:00:00 AM
Firstpage :
1023
Lastpage :
1028
Abstract :
Shift Walsh matrix is first introduced. The 
shift Walsh matrix is formed from the Walsh matrix by shifting the columns of the Walsh matrix to the right, dropping the last 
columns and assigning first 
columns of the new matrix as zero elements. Delay Walsh functions can be expanded in terms of Walsh functions using shift Walsh matrix. Therefore, linear delay-differential equations can he analyzed by Walsh series approximation. The method is most useful for time-varying systems.
shift Walsh matrix is formed from the Walsh matrix by shifting the columns of the Walsh matrix to the right, dropping the last columns and assigning first columns of the new matrix as zero elements. Delay Walsh functions can be expanded in terms of Walsh functions using shift Walsh matrix. Therefore, linear delay-differential equations can he analyzed by Walsh series approximation. The method is most useful for time-varying systems.Keywords :
Delay systems; Linear systems, time-invariant continuous-time; Linear systems, time-varying continuous-time; Walsh series; Chemical engineering; Delay effects; Delay lines; Equations; Linear systems; Power engineering and energy; Stability; Symmetric matrices; Time series analysis; Time varying systems;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1978.1101888
Filename :
1101888
Link To Document :
