Actuator and sensor faults estimation for discrete-time descriptor linear parameter-varying systems in finite frequency domain

This paper investigates the problem of fault estimation for discrete-time descriptor linear parameter-varying systems with actuator faults, sensor faults and external disturbances. First, in order to estimate the actuator and sensor faults simultaneously, an augmented system is constructed, where the auxiliary state vector consists of the original state vector and the sensor fault vector. Then, considering the fact that many faults usually occur in finite frequency ranges, a novel fault estimation observer with finite frequency specifications is designed, where the conservatism can be reduced compared with the traditional fault estimation design methods in full frequency domain. By employing the generalised Kalman–Yakubovich–Popov lemma and two finite frequency H ∞ performance indices, the sufficient conditions of the proposed observer are given in terms of linear matrix inequalities. Furthermore, by using slack variables, improved results on the fault estimation observer design are obtained, which are convenient to calculate fault estimation observer parameters for different frequency ranges. An example is presented to illustrate the effectiveness of the proposed method.