Stochastic bounded real lemma and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e259" altimg="si7.svg"> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> control of difference systems in Hilbert spaces