Abstract: In this paper we discuss a numerical method for constructing feedback control laws which are robust with respect to disturbances or structured uncertainties. The idea of treating the control and disturbance as competing players in a differential game is well known (see [Basar, T. and Bernhard, P., $H_{\infty}$ Optimal Control and Related Minimax Design Problems, Birkhauser, Boston, 1991] for example) and leads to a non standard algebraic Riccati equation. We show that known convergence results for the standard linear quadratic regulator problem may be implemented and used as the basis for a numerical method for constructing control laws. For the case of structured uncertainties, we show that recent results of Speyer and Rhee [Rhee, I. and Speyer, J.L., ``A Game Theoretic Controller for a Linear Time-invariant System with Parameter Uncertainty and its Application to the Space Station'', AIAA paper number AIAA-90-3220-CP, 1990] for the finite dimensional case can be extended to infinite dimensions. Their approach is to take advantage of the factorization of the structured uncertainty so that the uncertainty is treated as a disturbance. Then the differential game framework is applied.