We　endeavor　to　investigate　the　H-infinity　synthesis　problem　of　switched　fuzzy　systems　composed　by　several　discrete-time　subsystems.　By　designing　a　novel　QTD-MD　Lyapunov　function,　novel　criteria　assuring　stability　as　well　as　an　expected　H-infinity　performance　are　first　developed.　Based　on　these　sufficient　conditions,　some　other　conditions　for　solving　the　fuzzy　H-infinity　controllers　are　derived　subsequently.　Furthermore,　the　criteria　are　given　as　LMIs,　thus　the　implementations　are　easy　to　execute.　Simulations　are　also　provided　to　confirm　the　feasibility　of　the　presented　strategy.　(C)　2020　ISA.　Published　by　Elsevier　Ltd.　All　rights　reserved.