Parametric methods for pole assignment

The non-redundant parametrization of the pole assignment problem for a n-th order system with m inputs allows to express the solution of the problem in term of n(m - 1) free parameters. These parameters can be used to fulfill additional requirements on the closed-loop system as for instance minimum norm feedback gain matrix, well conditioned eigenvector set, maximum stability radius. One of reliable numerical methods for pole assignment is the so-called Schur method. An extension of this method is proposed which computes the solution of the pole assignment problem corresponding to a non-redundant parameter set. Several possibilities are further investigated to compute minimum norm feedback matrices. An improved approach to compute minimum Frobenius-norm feedback relying on a redundant parametrization is also discussed.