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

Amaury Hayat; Peipei Shang

doi:10.1016/j.automatica.2018.10.035

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

Amaury Hayat
, Peipei Shang

UPMC Université de Paris VI
ETH Zurich
Lamsid/EDF/R and D
Tongji University

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

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 H²-norm is guaranteed.

Original language	English
Pages (from-to)	52-60
Number of pages	9
Journal	Automatica
Volume	100
DOIs	https://doi.org/10.1016/j.automatica.2018.10.035
Publication status	Published - 1 Feb 2019
Externally published	Yes

Keywords

Asymptotic stabilization
Inhomogeneous
Lyapunov
Robust control of nonlinear systems
Saint-Venant equations

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10.1016/j.automatica.2018.10.035

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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 H2-norm is guaranteed.",

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AU - Shang, Peipei

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N2 - 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.

AB - 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.

KW - Asymptotic stabilization

KW - Inhomogeneous

KW - Lyapunov

KW - Robust control of nonlinear systems

KW - Saint-Venant equations

UR - https://www.scopus.com/pages/publications/85056903661

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DO - 10.1016/j.automatica.2018.10.035

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SN - 0005-1098

VL - 100

SP - 52

EP - 60

JO - Automatica

JF - Automatica

ER -

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

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Keywords

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