DocumentCode :
853094
Title :
A property of internally balanced and low noise structures
Author :
Williamson, Darrell
Author_Institution :
Australian National University, Canberra, Australia
Volume :
31
Issue :
7
fYear :
1986
fDate :
7/1/1986 12:00:00 AM
Firstpage :
633
Lastpage :
634
Abstract :
Given an 
th-order minimal asymptotically stable system 
, we consider the class 
of minimal state-space realizations which minimize the trace of 
, where 
is the controllability and 
the observability Grammian. We show that the optimal structures are defined by 
with optimal cost 
where 
is the sum of singular values. For 
, the internally balanced structure belongs to while if 
, the optimal noise structures of Mullis and Roberts [1] belong to . In particular, both structures are optimal when and 
.
th-order minimal asymptotically stable system , we consider the class of minimal state-space realizations which minimize the trace of , where is the controllability and the observability Grammian. We show that the optimal structures are defined by with optimal cost where is the sum of singular values. For , the internally balanced structure belongs to while if , the optimal noise structures of Mullis and Roberts [1] belong to . In particular, both structures are optimal when and .Keywords :
Asymptotic stability, linear systems; Controllability, linear systems; Observability, linear systems; Reduced-order systems, linear; Controllability; Cost function; Digital filters; Filtering; Matrix decomposition; Noise reduction; Observability; Optimal control; Quantization; Systems engineering and theory;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1986.1104351
Filename :
1104351
Link To Document :
