Parametric eigenstructure assignment by state feedback in descriptor systems

A new complete parametric approach for eigenstructure assignment in the descriptor linear system Ex = Ax + Bu via state feedback control u = Kx is presented. Based on a proposed complete parametric solution to the generalised Sylvester matrix equation, explicit parametric forms of the closed-loop eigenvectors and the feedback gain matrix are given. The approach involves mainly a series of singular value decompositions, and is thus numerically simple and reliable. The approach assigns arbitrary rank(f) finite relative eigenvalues to the closed-loop system and guarantees the closed-loop regularity. A numerical example is worked out to demonstrate the effect of the proposed approach.