DocumentCode :
806350
Title :
A characterization of eAtand a constructive proof of the controllability criterion
Author :
Vidyasagar, M.
Author_Institution :
Sir George Williams University, Montreal, P. Q., Canada
Volume :
16
Issue :
4
fYear :
1971
fDate :
8/1/1971 12:00:00 AM
Firstpage :
370
Lastpage :
371
Abstract :
A differential equation characterizing the functions 
, which arise when eAtis expressed as 
, is derived. It is shown that the set of functions 
is linearly independent over any nonzero interval. Using this fact, a constructive proof is given for the well-known criterion for a linear time-invariant system to be controllable, namely, rank ![[B|AB| ... |A^{n-1}B] = n](/images/tex/4165.gif)
.
, which arise when eAtis expressed as , is derived. It is shown that the set of functions is linearly independent over any nonzero interval. Using this fact, a constructive proof is given for the well-known criterion for a linear time-invariant system to be controllable, namely, rank .Keywords :
Controllability; Linear systems, time-invariant continuous-time; Matrix functions; Analog computers; Automatic control; Computational Intelligence Society; Control systems; Controllability; Differential equations; Polynomials; Sufficient conditions; Testing;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1971.1099751
Filename :
1099751
Link To Document :
