Observer design for discrete-time linear systems with unknown disturbances

In this paper, a novel unknown input observer is proposed for discrete-time linear systems. Without using similarity transformations, a slightly modified model of the system is obtained and then an observer is designed for the modified model. The proposed approach performs state and input estimation at the same time, which can be crucial in fault detection applications. Based on the linear system theory, necessary stability conditions are established and then a Lyapunov-based approach is taken to obtain the design LMI´s. Simulation results are used to illustrate the effectiveness of the proposed observer.