This paper deals with Hinf observer-based feedback control for linear time-delay systems, in the framework of delay independent stability. We will propose a new LMI solution to observer-controller design that ensures a disturbance attenuation level for the controlled output as well as for the state estimation error, which is an open problem. This will be compared with a well-known solution and with a usual strategy in control which consists in designing the observer and the controller separately. Our aim is to try to bring a positive answer to the following question: is there an interest to solve the problem in a single (unique) formulation or should we design separately the observer and the controller? An application to a wind tunnel model is provided to emphasize the interest of the given results, particularly in comparison with existing results on Hinf observer-based control.