An optimization approach for worst-case fault detection observer design

This paper deals with the fault detection problem for linear system with unknown inputs. The H∞, norm and H_ index are employed to measure the robustness to unknown inputs and the fault sensitivity, respectively. Furthermore, by using the pole assignment approach, the fault detection problem is transformed to an unconstrained optimization problem. With the aid of the gradient-based optimization approach, an explicit formula for designing the desirable observer gain is derived. On the other hand, the fault sensitivity over a finite frequency range can also be solved by the proposed method, in which case no constraint is required on D being of full column rank for a system (A, B, C, D). Numerical simulation has demonstrated the effectiveness of the present methodology.