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

Explicit boundary dissipative conditions are given for the exponential stability in L2L2-norm of one-dimensional linear hyperbolic systems of balance laws ∂tξ+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.