A block Arnoldi based method for the solution of the Sylvester-observer equation. ETNA - Electronic Transactions on Numerical Analysis

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