DocumentCode :
805501
Title :
Finite series solutions for the transition matrix and the covariance of a time-invariant system
Author :
Bierman, G.J.
Author_Institution :
Litton Systems Inc., Woodland Hills, CA, USA
Volume :
16
Issue :
2
fYear :
1971
fDate :
4/1/1971 12:00:00 AM
Firstpage :
173
Lastpage :
175
Abstract :
The transition matrix 
corresponding to the 
-dimensional matrix 
can be represented by 
, where the vector 
is generated from 
and Ac is the companion matrix to . The result is applied to the covariance differential equation 
and its solution is written as a finite series. The equations are presented in a form amenable for implementation on a digital computer.
corresponding to the -dimensional matrix can be represented by , where the vector is generated from and A . The result is applied to the covariance differential equation and its solution is written as a finite series. The equations are presented in a form amenable for implementation on a digital computer.Keywords :
Covariance matrices; Linear systems, time-invariant continuous-time; Matrix functions; Control systems; Covariance matrix; Differential equations; Eigenvalues and eigenfunctions; Estimation theory; Frequency domain analysis; Linear systems; Stochastic systems; Symmetric matrices; Time domain analysis;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1971.1099668
Filename :
1099668
Link To Document :
