Facing to a class of actuator faults and sensor faults with known dynamic characteristics but unknown initial conditions for linear systems with multiple disturbances, the fault detection and isolation (FDI) problems are considered based on the reduced dimensional state observer. This approach has simpler construction, less computation and quicker response speed, and this approach is more easily understood and designed. Making use of the result of fault detection, the fault self-restore controller and the feedforward control law are designed to make the system work normally with faults, i.e., faults are isolated. According to the pole assignment, the system with faults may have expected performance indexes. An example is used to demonstrate that the FDI scheme and the control law are efficient.