Eigenstructure assignment in linear multivariable systems--A parametric solution

This paper generalizes a recently reported method [1] of closed-loop eigenstructure assignment via state feedback in a linear multivariable system (with
n
states and
r
control inputs). By introducing a lemma on the differentiation of determinants, the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of
n r
-dimensional free parameter vectors. This parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue-assignment problem and thereby provides an efficient means of further modifying the system dynamic response. A numerical example is worked out to demonstrate the feasibility of the method.