The discrete-time H∞ control problem with strictly proper measurement feedback

This paper is concerned with the discrete-time H_∞ control problem with strictly proper measurement feedback. The authors derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given H_∞ 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, the authors give an explicit formula for one controller which achieves this bound.