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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 18-36, 2017/11/07
This paper describes a new block method for solving multi-input Sylvester-observer equations that arise in the construction of the well-known Luenberger observer. The proposed method is based on the block Arnoldi process and generalizes to the multi-input case, the method proposed by Datta and Saad for the single input Sylvester-observer equation. We give new algebraic properties and show how to construct the Luenberger observer by solving a special large-scale Sylvester equation for which two unknown matrices are to be computed. The numerical tests show that the proposed approach is effective and can be used for large-scale Luenberger observer problems.
Keywords: Block Arnoldi process, Luenberger-observer, Sylvester equation