Parametric approaches for ESA in discrete time-delay systems via memory state feedback

This paper proposes a memory state feedback controller for discrete time-delay systems based on the state feedback eigenstructure assignment (ESA) result for high-order linear systems [1-2]. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two complete 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 expression for the feedback gains and the closed loop eigenvector matrices. The first one mainly depends one a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the systems, 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.