inverse eigenvalue problem

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper a new method for eigenvalue assignment of discrete-time linear systems with state and input time-delays by static output feedback matrix is presented. The main result is an iterative method that only requires linear equations to be solved at each iteration. In this scheme, first a linear delayed system by defining an augmented vector is changed to standard form, then output feedback matrix K is calculated by inverse eigenvalue problem. We investigate all types of delays in the states, inputs or both for discrete – time linear systems. A simple algorithm and an illustrative example are presented to show the advantages of this new technique.