The discrete-time $H_\infty$ control problem with strictly proper measurement feedback

This paper is concerned with the discrete-time H8 control problem with strictly proper measurement feedback. We derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given H8 norm bound. Note that contrary to the continuous time, in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator. Finally, we give an explicit formula for one controller which achieves this boun