A　controller　design　is　proposed　for　networked　control　systems　with　two　types　of　random　communication　delays.　One　is　from　the　controller　to　the　actuator,　and　the　other　is　from　the　sensor　to　the　controller,　via　a　limited　bandwidth　communication　channel.　The　random　delays　are　modeled　as　a　binary　switching　sequence　satisfying　a　Bernoulli　distribution.　We　present　a　sufficient　condition,　in　the　form　of　matrix　inequalities,　for　the　existence　of　a　dynamic　output　feedback　controller　which　makes　the　closed-loop　system　exponentially　mean-square　stable　with　a　prescribed　H-infinity　performance.　The　sequentially　linear　programming　matrix　method　(SLPMM)　is　applied　to　solve　the　matrix　inequalities.　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.