Abstract
Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a bounded interval are investigated. The main result is to show that the existence of a 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 stabilising linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilisation of open channels represented by Saint-Venant equations with non-uniform steady-states. Copyright © IFAC 2010
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