Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment

AbstractWe propose an Arnoldi-based numerical method for solving a Sylvester-type equation arising in the construction of the Luenberger observer. Given an N×N matrix A and an N×m matrix G, the method simultaneously constructs an m×m Hessenberg matrix H with a preassigned spectrum and an N×m orthonormal matrix X such that AX−XH=G. We consider the case when A is large and sparse, so that the standard techniques such as the well-known Hessenberg-Schur method for solving a Sylvester equation cannot be easily applied. As a byproduct, we propose an algorithm for the partial pole-assignment problem for large matrices