A matrix method is introduced for determination of robust-stability zones of the general linear time invariant discrete-time dynamics with large delays against parametric uncertainties. The technique employs Kronecker Product and unique properties of palindrome polynomials, which are subset of self-inversive polynomials. These polynomials possess interesting features on the distribution of its zeros. The main motivation in this chapter is to develop a practical tool for determination of robust stability zones against parametric uncertainties and dominant pole assignment of systems in discrete-time domain. A sufficient condition for robust stability and dominant pole assignment is presented. The procedure for the solution is demonstrated via some example case studies.