Mixed H2/H∞ control: the discrete-time case

A stochastic H_∞ and a mixed stochastic H₂/H_∞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 H₂-type minimization problem and the H_∞- type constraint influence each other.