A stochastic H/sub /spl infin// and a mixed stochastic H/sub 2//H/sub /spl infin//control problem for discrete-time systems are considered and solved. Conditions for existence of a solution are derived, based on the solvability of an equivalent minimax problem. In this framework, it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects. The controller can be designed by solving a system of three coupled Riccati equations. Such equations display how the H/sub 2/-type minimization problem and the H/sub /spl infin//- type constraint influence each other.