Automatica, Vol.100, 52-60, 2019
A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope
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. (C) 2018 Elsevier Ltd. All rights reserved.