Observer design and stabilization of the dominant state of discrete-time linear systems

In this paper, we present necessary and sufficient conditions for both observer design and stabilization of the dominant state of discrete-time linear systems. Our method essentially uses the model reduction of the original linear control system. We also establish a separation principle so that when the reduced-order plant is stabilizable, the state of the reduced order observer may be used in lieu of the state of the reduced order plant for implementing the stabilizing state feedback control law. The model reduction and the observer design detailed in this paper are discrete-time analogs of the results of Aldeen and Trinh (1994) for continuous-time linear systems.