Conditions
for boundary feedback stabilizability of non-uniform linear 2 × 2
hyperbolic systems over a bounded interval are investigated. The main
result is to show that the existence of a basic quadratic control
Lyapunov function requires that the solution of an associated ODE is
defined on the considered interval. This result is used to give
explicit conditions for the existence of stabilizing linear boundary
feedback control laws. The analysis is illustrated with an application
to the boundary feedback stabilization of open channels represented by
linearized Saint–Venant equations with non-uniform steady-states.