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 N th-order minimal asymptotically stable system H(z) , we consider the class e of minimal state-space realizations which minimize the trace of \\gamma ^{2}K + W , where K is the controllability and W the observability Grammian. We show that the optimal structures are defined by W = \\gamma ^{2}K with optimal cost 2\\gamma S where S is the sum of singular values. For \\gamma = 1 , the internally balanced structure belongs to e while if \\gamma = S/ N , the optimal noise structures of Mullis and Roberts [1] belong to e . In particular, both structures are optimal when \\gamma = 1 and S = N .
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 :
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