Applying discrete-time proportional integral observers for state and disturbance estimations

In this note, we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete-time nonminimum phase systems. Conditions for providing the existence of such observer are given. When the disturbances do not vary too much between two consecutive sampling instances, the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region. Simulation results support the theoretical developments.