Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws

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 ∂ x ξ − M ξ = 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.