Robust fault detection for uncertain discrete-time systems

The fault detection problem under structured uncertainties in the system matrices is considered. The sensitivity of robust fault detection is one of the important issues considered in the fault detection and isolation development. To enhance this characteristic, an unconstrained optimization approach is taken to design a robust fault detection observer. The approach aims at enhancing the fault detection robustness to uncertainties without sacrificing the fault detection sensitivity, which was seldom addressed before. Furthermore, other objectives related to the observer gain and the eigenstructure conditioning of the observer system are also taken into account. The gradient-based optimization approach is facilitated by the explicit gradient expressions derived. Numerical simulation has also demonstrated the tradeoffs between different objectives as well as the effectiveness of the present methodology.