A unified framework for simultaneous fault and state estimation of linear discrete-time descriptor stochastic systems in the presence of the unknown disturbances

This paper considers the problem of simultaneously estimating the state and the fault of Direct Current (DC) motor in light of the recursive optimal filtering framework. A possible solution to solve this problem is to develop a robust three-stage kalman filter structure to obtain an unbiased minimum variance state and fault estimation via decoupling the unknown disturbances. The proposed filter serves as an extension to the recently designed robust two-stage kalman filter for the descriptor systems. Afterward, a descriptor stochastic model of the DC motor is proposed. This descriptor form can simultaneously express the dynamic and the constraints of the system. Furthermore, it is shown that the obtained descriptor model of the DC motor can be equivalently transformed into an equivalent standard state-space system where the actuator and sensor fault affects both the state and output equations, respectively. Whereas the disturbances only affect the state equation. The direct feedthrough matrix distribution of the fault which is assumed to be of an arbitrary rank. Finally, an application of DC motor is included to show the efficiency of the proposed filter.