A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope

• Autores: Amaury Hayat, Peipei Shang
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 100, 2019, págs. 52-60
• Idioma: inglés
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• Resumen

  • The exponential stability problem of the nonlinear Saint-Venant equations is addressed in this paper. We consider the general case where an arbitrary friction and space-varying slope are both included in the system, which lead to non-uniform steady-states. An explicit quadratic Lyapunov function as a weighted function of a small perturbation of the steady-states is constructed. Then we show that by a suitable choice of boundary feedback controls, that we give explicitly, the local exponential stability of the nonlinear Saint-Venant equations for the H2-norm is guaranteed.