Abstract
A new complete parametric approach for eigenstructure assignment in the descriptor linear system Eẋ=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(E) 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.
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