Design of full order proportional-integral observer for the state estimation of discrete-time linear time-invariant systems

This paper is devoted to the design of full order proportional-integral observer for the state estimation of discrete-time linear time-invariant systems. In particular, explicit necessary and sufficient conditions are established for the existence of proportional-integral observer for the state estimation of discrete-time linear time-invariant systems and a simple procedure is given for the construction of the observer. Our approach is based on properties of real and polynomial matrices.