The　robust　H∞　filtering　problem　is　considered　for　discrete-time　systems　subject　to　norm-bounded　parameter　uncertainties　in　both　the　state　and　the　output　matrices　of　the　state-space　model.　Sufficient　conditions　for　the　filter　to　satisfy　prescribed　H∞　performance　and　steady-state　estimation　error　variance　constraints　are　given　in　terms　of　two　discrete　algebraic　Riccati　inequalities.　The　filter　obtained　does　not　depend　on　the　perturbation　parameter　which　is　assumed　to　be　unmeasured.　An　example　is　provided　to　illustrate　the　use　of　the　results　for　filter　design.