Robust and well‐conditioned eigenstructure assignment via sylvester's equation

Abstract

Abstract An algorithmic solution is given for 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 A + BF to have low eigenvalue sensitivity. The algorithm relies on a solution of Sylvester's equation and does not involve co‐ordinate transformations or canonical forms. These results are steps in the direction of transforming pole assignment theory into an effective design tool for control systems.