Abstract: In order to improve both robustness against disturbances and sensitivity against faults and reduce the design conservativeness for the model uncertainties and unknown inputs, a design method of the H-/H∞fault detection observer is presented in this paper, the non convex constraint formulations can be converted into linear matrix inequality(LMI) constraints through lossless S procedure, the design of the H-/H∞fault detection observer can be transformed into the convex optimization problems with LMI constraints by making use of Schur theorem. The adaptive threshold generators are designed for decreasing the rates of false alarming. According to the numerical calculation of the convex optimization problems, the design of the fault detection observer process can be easy to achieve. The proposed algorithms guarantee the optimization trade\|off between the robustness to the unknown inputs and the sensitivity to faults. Simulation shows that the proposed algorithms ensure the convergence of the residuals quickly and decrease the fault detection time.

Key words: Fault detection, LMI, Design of observer, Robustness