Pseudo-predictor feedback control of discrete-time linear systems with a single input delay

This paper studies the problems of stabilization of discrete-time linear systems with a single input delay. By developing the methodology of pseudo-predictor feedback (PPF) which uses the (artificial) closed-loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed-loop system in terms of the stability of a class difference equations. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open-loop system is only polynomially unstable. Numerical examples show the effectiveness of the proposed approaches.