A combined cost function is posed which includes both H∞sensitivity and disturbance minimization terms, as well as minimum variance tracking error and control signal terms. In some problems the criterion represents the engineering requirements of the designer more realistically than H∞or linear quadratic gaussian (LQG) cost lerms alone. The solution to the combined cost function problem is obtained by using a H∞‘embedding procedure’. This subsumes the H∞part of the problem within a fictitious LQG cost function minimization problem. The selection of the cost function weights to achieve certain design requirements is discussed and a method is proposed which leads to very simple computational procedures. In fact, the computation of the two controllers does not involve an iterative method and only requires the solution of a standard spectral factorization and diophantine and eigenvector equations.