State and Faults Interval Estimations for Discrete-time Linear Systems

This paper concerns state and fault simultaneous interval estimations for discrete-time linear systems with unknown but bounded uncertainties. Unlike most existing works on interval estimation, the system considered in this work is subject to actuator and sensor faults, while bounded uncertainties exist in both components. Thus, the method developed in this paper can be used for more general conditions. First, the considered system is reformulated as a descriptor one through the augmented vector method. An important lemma for descriptor systems is given in a more accurate description and proven in a very simple way. Then, by using the reachability analysis technique, a new proportional-integral observer-based interval estimation method is proposed. The H-infinity technique reduces the influences of time-varying actuator faults and uncertainties. To build the zonotope of bounded uncertainties in the residual system, an equivalent description is introduced. Finally, a numerical example and an industrial system are simulated to demonstrate the efficacy and applicability of the developed method.