Robust observer-based sensor fault reconstruction for discrete-time systems via a descriptor system approach

This paper addresses the problem of observer-based sensor fault reconstruction for discretetime systems subject to external disturbances via a descriptor system approach. First, an augmented descriptor system is formulated by letting the sensor fault term be an auxiliary state vector; then a discrete-time descriptor state observer is constructed to achieve concurrent reconstructions of original system states and sensor faults. Sufficient and necessary conditions for the asymptotic stability of the proposed observer are explicitly provided. To broaden its application scope, less restrictive existence conditions are further discussed. Further, sufficient conditions for the robust stability of the proposed observer are formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved using LMI optimization techniques. After that, an extension of the proposed linear approach to discretetime nonlinear systems with Lipschitz constraint is investigated. At last, two illustrative examples are given to verify the effectiveness of the proposed techniques.