This　paper　considers　the　consensus　of　a　class　of　nonlinear　dynamical　networks,　and　the　subsystems　are　discrete　time　pendulum-like　systems.　Two　kinds　of　interconnections　are　considered　in　view　of　the　fact　that　the　subsystems　of　networks　may　have　more　than　one　kind　of　interconnection　between　each　other.　A　linear　transformation　is　used　to　transform　the　consensus　problem　to　the　partial　stability　problem　of　a　corresponding　system.　Sufficient　and　necessary　conditions　for　consensus　are　given　for　the　nonlinear　dynamical　networks　based　on　the　Lyapunov　theory　and　S-procedure.　The　Kalman-Yakubovich-Popov　(KYP)　lemma　is　applied　to　get　the　frequency　domain　criterion.　The　test　of　the　consensus　of　a　network　of　pendulum-like　systems　is　separated　into　the　tests　of　the　absolute　stability　of　several　independent　pendulum-like　systems.　Furthermore,　a　controller　design　method　based　on　LMIs　is　provided.　Finally,　a　numerical　example　is　given　to　illustrate　the　efficiency　and　applicability　of　the　proposed　methods.