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A property of internally balanced and low noise structures

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1 Author(s)
Williamson, D. ; Australian National University, Canberra, Australia

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 .

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Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 7 )