Design of observers with arbitrary exponential convergence rate for discrete-time descriptor systems

This paper presents a new state observer for linear discrete-time descriptor systems. By employing the Lyapunov theory, it is proven that if the five coefficients of the proposed observer satisfy the three given matrix equations then the observer has an exponential convergence that its rate is chosen by designer. The mentioned three matrix equations are analyzed, and the procedure of determining observer coefficients is described in details. A numerical example is given to show the design method and illustrate the effectiveness of the proposed observer.