In　this　paper,　a　new　discrete-time　dynamic　game　where　two　players　seek　to　reinforce　and　suppress　the　output　of　a　system　under　the　influence　of　a　known　deterministic　input　is　considered.　A　necessary　and　sufficient　condition　for　the　existence　of　a　saddle-point　solution　to　this　game　is　derived　in　terms　of　a　discrete-time　Riccati　difference　equation.　The　result　of　the　game　is　used　to　solve　the　robust　H∞　filtering　problem　for　discrete　time-varying　systems　subject　to　a　known　deterministic　input　and　norm-bounded　parameter　uncertainties　occurring　in　both　the　state　and　the　output　matrices　of　the　state-space　model.　There　is　no　restriction　on　the　form　of　the　filter.　This　allows　the　effect　of　the　known　input　on　the　estimation　error　due　to　system　uncertainties　to　be　optimally　reduced　without　any　prior　assumption　on　the　filter　structure.