Partial eigenstructure assignment by state feedback: A complete parametric approach

This paper treats the problem of partial eigenstructure assignment by state feedback in controllable, time-invariant, multivariable linear systems. The aim is to assign only a subset of the closed-loop eigenvalues with arbitrary multiplicities, together with their right eigenvectors and eigenvector chains, while leaving the rest unchanged from the open-loop. With the help of a complete parametric solution to the generalised Sylvester matrix equation AV+BW=VF, simple, complete, parametric expressions are established for the assigned closed-loop eigenvectors and the feedback gain.