Abstract: The robust fault detection filter design problem for state-delay systems with disturbance is studied in this paper. By combining the appropriate input/output channels, a performance index is introduced, which simultaneously takes into account the robustness of the fault detection observer against disturbance and sensitivity to faults. The observer-based robust fault detection filter problem is formulated as an H1 optimization problem. Using linear matrix inequality techniques, the solvable condition of this optimization problem and further the solutions are derived. Finally, the validity of this approach is illustrated by a numerical example.