Robust and Well Conditioned Eigenstructure Assignment via Sylvester´s Equation

In this paper we present an algorithmic solution to the problem of calculating a pole assignment matrix F that makes the eigenvector matrix of A+BF well conditioned with respect to inversion, or equivalently maximally orthonormal. This causes AMBF to have low eigenvalue sensitivity. The algorithm relies on solution of Sylvester´s equation and does not involve coordinate transformations or canonical forms. These results are the first steps in the direction of transforming pole assignment theory into an effective design tool for control systems.