In this paper, the problem of control reconfiguration in the presence of actuator failure preserving the nominal controller is addressed. In the actuator failure condition, the processing algorithm of the control signal should be adapted in order to re-achieve the desired performance of the control loop. To do so, the so-called reconfiguration block, is inserted into the control loop to reallocate nominal control signals among the remaining healthy actuators. This block can be either a constant mapping or a dynamical system. In both cases, it should be designed so that the states or output of the system are fully recovered. All these situations are completely analysed in this paper using a novel structural approach leading to some theorems which are supported in each section by appropriate simulations.