On boundary feedback stabilization of non-uniform linear hyperbolic systems over a bounded interval

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.