In this paper, we consider fault detection, isolation and reconstruction problem for descriptor systems with actuator faults and sensor faults, respectively. When actuator faults exist in the system, the fault detection and isolation (FDI) problem is solved through an unknown input observer regarding remaining faults excluded a specified fault as unknown inputs. Whereas, in existing sensor faults, the fault detection is only achieved by the unknown input observer and residual signals. Since the derivative signal of sensor fault is generated in the error dynamics between the actual system and the derived observer. The main objective of this work attempts the reconstruction of the faults. The reconstruction can be achieved by sliding mode observer including feedforward injection map and compensation signal. Finally, the isolation problem of sensor faults is solved by reconstructing all of the faults.