ESA for a type of discrete time-delay linear system via state feedback

In this paper the state feedback controller for a type of discrete time-delay linear system is proposed, based on the eigenstructure assignment (ESA) approach. Using the right coprime factorization a set of analytic and parametric solution to the established high-order Sylvester matrix equation is obtained. Further a set of parametric solution for the proposed eigenstructure assignment problem is presented. This method gives a complete parametric expression for the closed-loop eigenvectors matrix and the feedback gain matrices. An example illustrates the effect of the proposed approach.