The stability analysis of the adaptive three-stage Kalman filter

•Consider the incomplete model of fault and unknown inputs.•Use three-stage U–V transformation and adaptive forgetting factor techniques.•We propose an adaptive three-stage Kalman filter tracking the fault and unknown inputs in general models of fault and unknown inputs.•Its detailed stability analysis has been proved.

An adaptive three-stage Kalman filter, which can track the fault and unknown inputs, is proposed by extending the special linear models of fault and unknown inputs to two general linear models without requirement of matrices ranks. It can be used when the fault and unknown inputs are not perfectly known. In this paper, the detailed stability analysis of the adaptive three-stage Kalman filter, which is applied for state and fault estimation of linear systems in the presence of unknown inputs, is investigated. Furthermore, an illustrative example is given to apply this filter and the performances of this filter are also verified by simulation.