In　this　paper,　we　propose　a　novel　robust　H-infinity　optimization　approach　to　the　design　of　digital　filters　for　calibrating　2-1　cascaded　sigma-delta　(SD)　modulators.　The　main　contribution　of　this　paper　consists　of　two　parts.　First,　we　develop　a　new　filter　design　technique　based　on　linear　matrix　inequalities　applied　to　a　model-matching　problem　with　polytopic　uncertainties　in　parameters.　The　advantage　of　the　proposed　method　is　that　it　leads　to　an　optimal,　less　conservative,　solution　to　the　robust　H-infinity　filtering　problem.　The　second　contribution　involves　the　application　of　the　proposed　robust　filter　design　scheme　to　correct　for　inevitable　and　unwelcome　analog　imperfections　typically　associated　with　cascaded　SD　modulators.　For　numerical　illustration　we　concentrate　on　the　2-1　architecture.　Simulation　results　for　a　range　of　parameter　excursions　suggest　that　our　robust　H-infinity　filter　guarantees　an　improved　signal-to-noise　ratio　performance　over　the　nominal　filter.