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This paper considers eigenstructure assignment in high-order descriptor linear systems via proportional plus derivative state feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches

This paper considers eigenstructure assignment in high‐order linear systems via output feedback. Parametric expressions for the left and right closed‐loop eigenvectors associated with the finite closed‐loop eigenvalues and two simple and complete parametric solutions for the feedback gain matrices are obtained on the basis of the parametric solutions of the generalized high‐order Sylvester matrix equations. This approach does not impose any restrictions on the closed‐loop eigenvalues. An illustrative example shows the effect of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society