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 eta sufficient conditions for the existence of a-suboptimal controller are derived and the set of all linear time-invariant controllers, which solve the problem, is parametrized. In contrast with the unconstrained case, the state-space solution obtained is very transparent and actually is not more complex than the solution of the continuous-time H problem.