The　proportional-integral　(PI)　boundary　stabilization　of　nonlinear　hyperbolic　systems　of　balance　laws　is　investigated　for　the　H-2-norm,　in　which　the　control　and　output　measurements　are　all　located　at　the　boundaries.　The　boundary　conditions　of　the　system　are　subject　to　unknown　constant　disturbances.　The　induced　closed-loop　system　is　proven　to　be　locally　exponentially　stable　with　respect　to　the　steady　states.　To　this　end,　a　set　of　matrix　inequalities　is　given　by　constructing　a　new　Lyapunov　function　as　a　weighted　H-2-norm　of　the　classical　Cauchy　solution　and　the　integral　of　boundary　output.　Furthermore,　the　traffic　flow　dynamics　of　a　freeway　section　are　modeled　with　the　Aw-Rascle-Zhang　model.　To　stabilize　the　oscillations　of　traffic　demand,　a　local　PI　boundary　feedback　controller　is　designed　with　integration　of　on-ramp　metering　and　variable　speed　limit　control.　The　exponential　convergence　of　the　nonlinear　traffic　flow　dynamics　in　an　H-2　sense　is　achieved　and　validated　with　simulations.