Eigenstructure assignment in descriptor systems via output feedback: a new complete parametric approach

A complete parametric approach is proposed for eigenstructure assignment in descriptor linear systems via output feedback, which assigns arbitrary rank(E) finite relative eigenvalues to the closed-loop system and guarantees the closed-loop regularity. General parametric expressions for the normalized left and right closed-loop eigenvector matrices are obtained on the basis of a recent parametric solution for the generalized Sylvester matrix equation. These expressions contain two groups of parameter vectors which represent the degree of freedom existing in the solution of the closed-loop eigenvectors. A pair of general complete expressions for the output feedback gain is also presented, containing the part of parameter vectors existing in the closed-loop eigenvectors and another extra two parameter matrices. The sub-conventional case is especially treated, in which there exists a one-to-one mapping relation between the closed-loop eigenvector matrices and the output feedback gain. This approach does not impost any restriction on the closed-loop eigenvalues, but generalizes and improves some of the existing results. An illustrative example shows the effect of the proposed approach.