Eigenstructure assignment by decentralized output feedback-a complete parametric approach

The problem of eigenstructure assignment in multivariable linear systems by decentralized output feedback is considered. By using a complete parametric solution of a generalized Sylvester matrix equation, parametric representations of both the left and right closed-loop eigenvectors and generalized eigenvectors as well as the feedback gains with respect to the closed-loop eigenvalues and two series of partially free parameter vectors are established. The obtained result does not require any conditions on the closed-loop eigenvalues, and generalizes some previous results in this area. An example shows the effect of the proposed approach.>