Explicit
boundary dissipative conditions are given for the exponential stability
in L^2-norm of one dimensional linear hyperbolic systems of balance
laws ∂t ξ + Λ∂xξ −Mξ = 0 over a finite interval, when the matrix M is
marginally diagonally stable. The result is illustrated with an
application to boundary feedback stabilisation of open channels
represented by linearised Saint–Venant–Exner equations.