This paper deals with the problem of fault estimation for linear systems under feedback control. The main contribution is the development of a new method to simultaneously design two different systems as estimator and controller, which can achieve better detection performance and control performance compared with the known results. Low frequency faults and high frequency disturbances are considered, and the design schemes are presented in terms of solutions to a set of linear matrix inequalities(LMIs). A VTOL aircraft example is used to demonstrate the method and its effectiveness.