The solution to a linear quadratic stochastic optimal control problem is obtained for a discrete-time system. The performance criterion to be minimised includes the usual error and control weighting terms but has, in addition, the norms of the sensitivity and complementary sensitivity weighting matrices. The conditions for optimality are derived in the time-domain and the Wiener-type solution is obtained by transforming these conditions into thez-domain. A polynomial system description is then introduced so that the controller may be expressed in terms of the solution of diophantine equations. This is a more convenient form for computation of the controller.