LMI approach to H_/H _∞ fault detection observer design

Considering the effect of unknown input signals, the problem of a robust fault detection observer design for linear uncertain systems is investigated. The H_index and the H _∞ norm, which measure the sensitivity of the residual to the fault and the robustness of the effect of the unknown input on the residual, respectively, are used to describe the problem of this observer design as optimization problems. The existence conditions of such a fault detection observer are given in terms of matrix inequalities. The optimization observer gain is obtained by a new iterative linear matrix inequality (LMI) algorithm. The given example demonstrates that the designed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.