This paper proposes several design procedures for a class of novel unknown input observers (UIOs) to detect and isolate the actuator faults in finite frequency domain. Our approach dramatically reduces the number of UIOs required for multiple faults. Meanwhile, knowledge on the disturbance/noise is embedded to enhance the performance. All the design conditions are formulated in terms of LMI/BMI problems, which enable to consider other design specifications in addition to the robustness and sensitivity requirements.