The aim of this paper is to present new results on H ∞ control synthesis, via output-feedback, for time-delay linear systems. We extend the use of the finite order LTI system, called comparison system, to design a controller which depends not only on the output at the present time and maximum delay, but also on an arbitrary number of values between those. This approach allows us to increase the maximum stable delay without requiring any additional information. All methods presented here consider time-delay systems control design with classical numeric routines based on H ∞ theory. An illustrative example is presented.