Discrete-time PID observer design for state and unknown input estimations in noisy measurements

In response to MIMO discrete-time linear systems with unknown inputs and sensor noises, an observer algorithm which is capable of performing estimated system state and input disturbance is proposed in this paper. To effectively remove the effect of sensor noise, we transform the original model considered here into the descriptor form system. To effectively remove the effect of sensor noise, the original system is transformed into the descriptor system. Provided the variation of disturbance in the two consecutive sampling instances is not changed significantly and the system matrices satisfy the certain conditions, both the system state and the unknown input can be simultaneously estimated by the proposed proportional-integral-derivative observer algorithm. The estimation error can be constrained in a small bounded region of the order of O ( T ) where T is the sampling rate. Finally, a numerical example is presented to demonstrate the applicability of the proposed observer scheme.