This　paper　considers　the　global　convergence　of　a　class　of　nonlinear　dynamical　networks,　and　the　subsystems　are　discrete　time　pendulum-like　systems.　Different　from　most　of　the　existing　results,　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.　The　Kalman-Yakubovich-Popov　(KYP)　lemma　and　the　Schur　complement　formula　are　applied　to　get　novel　criteria,　which　have　the　forms　of　linear　matrix　inequalities　(LMIs).　The　Kronecker　product　is　presented　which　can　be　used　to　handle　a　class　of　LMI　problems.　The　test　of　the　global　convergence　of　a　network　of　pendulum-like　systems　is　separated　into　the　test　of　the　global　convergence　of　several　independent　pendulum-like　systems.　Furthermore,　a　controller　design　method　based　on　LMIs　is　provided.　Finally,　a　numerical　example　is　presented　to　illustrate　the　efficiency　and　applicability　of　the　proposed　methods.