On discrete-time H∞ problem with a strictly proper controller

In this paper the standard discrete-time H ∞ control problem is considered under the constraint imposed upon the controller to be strictly proper. The necessary and sufficient conditions for the existence of a γ-suboptimal controller are derived and the set of all LTI controllers, which solve the problem, is parametrized. In contrast with the unconstrained case, the state-space solution obtained is transparent and actually is not more complex then the solution of the continuous-time H ∞ problem.