Worst-case fault detection observer design: Optimization approach

This paper deals with the fault detection problem for linear systems with unknown inputs. The H _∞ norm and H _- index are employed to measure the robustness to unknown inputs and the sensitivity to faults, respectively. By using the pole assignment approach, the fault detection problem is transformed to an unconstrained optimization problem. With the aid of a gradient-based optimization approach, an explicit formula for designing the desirable observer gain is derived. Furthermore, the fault sensitivity over a finite frequency range can also be solved by the proposed method. The methodology proposed is verified through numerical simulation studies performed on the fault detection observer design of a vertical takeoff and landing aircraft.