In this paper, a method of generating robust residuals of a linear system, subject to unknown inputs, is proposed. The impact of disturbances and uncertainty may create difficulties at the decision stage of diagnosis (false alarm); this has resulted in the use of a robust observer for the unknown inputs to ensure the robustness of the system based on the unknown input observer with an optimal decoupling approach, which has a sensitivity that is minimal to unknown inputs and maximal to faults. A generation of robust residuals is then transformed into a problem of robustness/sensitivity constraints (H$_{\infty }$, H and then solved via a linear matrix inequality formulation by the solver CVX. An application for the method performance is also given.