DocumentCode :
855401
Title :
Lyapunov-like equations and reachability/observabiliy Gramians for descriptor systems
Author :
Bender, Douglas J.
Author_Institution :
Hughes Aircraft Company, Los Angeles, CA, USA
Volume :
32
Issue :
4
fYear :
1987
fDate :
4/1/1987 12:00:00 AM
Firstpage :
343
Lastpage :
348
Abstract :
Reachability and observability Gramians are defined for the descriptor systems 
and 
. The pencils 
and 
are assumed to be regular. If 
is singular,these Gramians do not, in general, satisfy the "expected" Lyapunov-like (Sylvester) equations (for example, 
if 
is the continuous-time teachability Gramian). This is shown by expressing the solution of the descriptor system in terms of the parameters of the Laurent expansion of 
or 
. We derive the Lyapunov-like equations which these Gramians do satisfy.
and . The pencils and are assumed to be regular. If is singular,these Gramians do not, in general, satisfy the "expected" Lyapunov-like (Sylvester) equations (for example, if is the continuous-time teachability Gramian). This is shown by expressing the solution of the descriptor system in terms of the parameters of the Laurent expansion of or . We derive the Lyapunov-like equations which these Gramians do satisfy.Keywords :
Linear systems; Lyapunov matrix equations; Observability, linear systems; Singular systems; Control systems; Controllability; Eigenvalues and eigenfunctions; Equations; Military aircraft; Observability; Stability;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1987.1104589
Filename :
1104589
Link To Document :
