On Lyapunov stability of linearised Saint-Venant equations for a sloping channel | Zendy

Georges Bastin | Zendy; JeanMichel Coron | Zendy; Brigitte d’Andréa-Novel | Zendy

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On Lyapunov stability of linearised Saint-Venant equations for a sloping channel

Author(s) -

Georges Bastin,

JeanMichel Coron,

Brigitte d’Andréa-Novel

Publication year - 2009

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2009.4.177

Subject(s) - dissipative system , lyapunov function , mathematics , cascade , stability (learning theory) , exponential stability , shallow water equations , norm (philosophy) , channel (broadcasting) , exponential function , flow (mathematics) , boundary (topology) , mathematical analysis , control theory (sociology) , computer science , physics , geometry , control (management) , nonlinear system , quantum mechanics , machine learning , computer network , chemistry , chromatography , artificial intelligence , political science , law

We address the issue of the exponential stability (in L-2-norm) of the classical solutions of the linearised Saint-Venant equations for a sloping channel. We give an explicit sufficient dissipative condition which guarantees the exponential stability under subcritical flow conditions without additional assumptions on the size of the bottom and friction slopes. The stability analysis relies on the same strict Lyapunov function as in our previous paper [5]. The special case of a single pool is first treated. Then, the analysis is extended to the case of the boundary feedback control of a general channel with a cascade of n pools

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