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

Amaury Hayat (1, 2) , Peipei Shang (3)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CaGE - Control And GEometry
3 School of Mathematical Sciences [Shanghai]

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 H 2-norm is guaranteed.

Mots clés: Asymptotic stabilization; Inhomogeneous; Saint-Venant equations; Lyapunov; Robust control of nonlinear systems

Domaines: Equations aux dérivées partielles [math.AP]

Amaury Hayat, Peipei Shang. A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope. Automatica, 2019, 100, pp.52-60. ⟨hal-01704710⟩