Under　the　condition　of　random　communication　delays,　the　H∞　state　feedback　problem　was　investigated　for　a　class　of　discrete　time　switched　systems　with　a　state-based　switching　law.　The　delay　of　data　packets　include　the　state　signal,　the　switched　signal　and　the　control　signal　and　the　delays　satisfy　the　Bernoulli　random　binary　distribution.　By　using　switched　Lyapunov　function,　the　state　feedback　controllers　for　each　subsystem　were　obtained.　The　closed-loop　systems　are　asymptotically　mean-square　stable　and　satisfy　the　prescribed　H∞　performance　constraint.　The　control　parameters　can　be　obtained　by　solving　a　set　of　linear　matrix　inequalities(LMIs).　Finally,　a　numerical　example　is　provided　to　illustrate　the　usefulness　of　the　proposed　design　method.