Fault detection observer design with unknown inputs

This paper deals with fault detection observer design for linear time-invariant systems with unknown inputs. The design objective is set to minimize a combined performance index H_infin/H_- which means to achieve a good compromise between robustness to the disturbance and sensitivity to the fault. Hence, the fault detection observer is designed to detect the fault of smallest energy possible. In this paper, the design for both static observer and more general dynamic observer is addressed. For the latter, change of variable method is used to make matrix inequality linear. In addition, a sequential linearization iterative LMI method is used to solve the nonconvex optimization, which guarantees the convergence