D - stability analysis for discrete system with time delay

By functional analysis and eigenvalue analysis methods in complex plane, several useful criteria are deduced which can guarantee that all the eigenvalues of discrete time-delay systems are located in a given region D(α, r) (with center (α,0) and radius r ) in the cases that the system matrix A is diagonalizable and A is a normal matrix. These criteria are simple to complete and can be used to solve the D - stability analysis problem for discrete time-delay systems, therefore they can optimize the dynamic performance of the system. The system is D - stable if the criteria are satisfied. And the criteria also can be applied to the case of real plane. Two examples are included to illustrate the effectiveness and feasibility of the criteria.