A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope. (February 2019)

• Record Type: Journal Article
• Authors: Hayat, Amaury; Shang, Peipei
• Is Part Of: Automatica. Volume 100(2019)
• Page Start: 52
• Page End: 60
• Publication Date: 2019-02
• Subjects: Asymptotic stabilization -- Lyapunov -- Saint-Venant equations -- Inhomogeneous -- Robust control of nonlinear systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.10.035
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.