This　paper　investigates　the　H∞　stability　and　consensus　of　uncertain　discrete-time　nonlinear　complex　dynamical　network　systems　based　on　T-S　fuzzy　model.　The　nonlinear　complex　dynamical　network　system　consists　of　N　nonlinear　discrete-time　subsystems.　Parallel　distributed　compensation　algorithm　and　Lyapunov　method　are　applied　to　design　an　H∞　decentralized　fuzzy　static　output　feedback　controller.　Based　on　Lyapunov　method,　a　static　output　feedback　controller　is　designed　to　guarantee　that　the　closed-loop　system　is　asymptotically　H∞　stable.　By　considering　the　characteristic　of　interconnection　matrix　of　the　network,　the　test　of　the　stability　of　the　network　system　is　separated　in　to　the　test　of　the　stability　of　the　several　nonlinear　systems.　Furthermore,　the　consensus　problem　for　the　leader-follower　complex　dynamical　network　is　considered.　And　the　proposed　criterion　can　be　obtained　by　solving　a　set　of　linear　matrix　inequalities(LMIs)　which　are　numerically　feasible.　The　effectiveness　of　the　proposed　methods　is　demonstrated　through　numerical　examples.　©　2015　IEEE.