Concerning　on　the　consensus　problem　of　a　networked　hyperbolic　system　of　two　linear　conservation　laws,　this　paper　proposes　a　boundary　consensus　protocol　and　establishes　a　theoretical　framework　for　consensus　analysis　under　both　fixed　and　switching　communication　topologies.　Firstly,　we　present　a　consensus　analysis　under　fixed　topologies　by　utilizing　the　Lyapunov　approach,　where　both　undirected　graph　and　digraph　cases　are　considered.　Under　the　assumption　that　the　undirected　graph　is　connected　or　the　digraph　is　balanced　and　rooted,　we　derive　sufficient　conditions　w.r.t.　the　boundary　control　matrices　and　Laplacian　eigenvalues　for　ensuring　the　asymptotic　consensus.　Secondly,　we　further　consider　the　consensus　problem　under　switching　topologies,　in　which　the　undirected　graph　(or　balanced　digraph)　is　relaxed　to　be　jointly　connected　(or　jointly　rooted).　By　using　the　Lyapunov　approach　combined　with　the　related　space　decomposition　technique,　we　derive　sufficient　conditions　w.r.t.　the　boundary　control　gain　based　on　a　priori　knowledge　of　possible　Laplacian　matrices　for　ensuring　the　asymptotic　consensus.　Finally,　we　provide　numerical　examples　and　an　application　to　the　consensus　control　of　a　multi-lane　road　traffic　flow　system　described　by　the　Aw-Rascle　Equations,　to　demonstrate　the　effectiveness　of　our　theoretical　results.　©　1963-2012　IEEE.