Asynchronous fault detection for switched positive systems by zonotopic residual evaluation

The present paper is devoted to the fault detection for discrete-time asynchronously positive switched systems with set-membership disturbances via a zonotopic residual assessment approach. Relative to existing studies, the developed scheme presents a time-varying threshold, which enhances detection sensitivity while guaranteeing disturbance robustness. Firstly, a criterion is established to ensure the stability and the mixed ℓ_∞/ℓ− performance of the augmented system. Subsequently, a co-design framework is constructed to tune the asynchronous fault detection observer for positive systems, along with switching laws for the considered system. In addition, a zonotopic residual set is designed to spatially encapsulate the feasible state evolutions of the faultless augmented system. Finally, the reliability of the proposed zonotope-based set-membership fault detection scheme is validated via a communication network model.