Volume 47, pp. 18-36, 2017.

A block Arnoldi based method for the solution of the Sylvester-observer equation

L. Elbouyahyaoui, M. Heyouni, K. Jbilou, and A. Messaoudi

Abstract

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.

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Key words

Block Arnoldi process, Luenberger-observer, Sylvester equation

AMS subject classifications

65F10

Links to the cited ETNA articles

[9]Vol. 33 (2008-2009), pp. 207-220 L. Elbouyahyaoui, A. Messaoudi, and H. Sadok: Algebraic properties of the block GMRES and block Arnoldi methods

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