The　robust　H-infinity　filtering　problem　with　error　variance　constraints　is　considered　for　discrete　time-varying　systems　subject　to　norm-bounded　parameter　uncertainties　in　both　the　state　and　the　output　matrices　of　the　state-space　model.　Sufficient　conditions　for　a　finite-horizon　filter　to　satisfy　state　estimation　error　variance　constraints　as　well　as　prescribed　H-infinity　performance　for　all　admissible　perturbations　are　given　in　terms　of　two　discrete　Riccati　difference　equations,　which　are　of　a　form　suitable　for　recursive　computation.　The　results　are　extended　to　cover　the　case　of　stationary　filtering　over　an　infinite-horizon　for　uncertain　time-invariant　systems.　(C)　2003　Elsevier　Science　Ltd.　All　rights　reserved.