Generalized Arnoldi methods for the Sylvester-observer equation and the multi-input pole placement problem

We propose a new generalized Arnoldi algorithm for constructing an orthogonal solution of the Sylvester-observer matrix equation arising in the design of Luenberger observer. The method in some sense, generalizes the single-output Datta-Saad method (1991) for the equation. The proposed algorithm is then conveniently used to develop a new algorithm for the multi-input pole placement problem. The results of our numerical experiments suggest that the algorithm is more efficient than some of the well-known algorithms for the problem.