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18th IFAC World Congress (IFAC WC 2011), Milan : Italie (2011)

Strict Lyapunov functionals for nonlinear parabolic partial differential equations

F. Mazenc 1, Christophe Prieur 2

(08/2011)

For families of partial differential equations (PDE) with particular boundary conditions, strict Lyapunov functionals are constructed. The PDE under consideration are parabolic and, in addition to the diffusion term, may contain a nonlinear source term plus a convection term. The boundary conditions may be either the classical Dirichlet conditions, or the Neumann boundary conditions or a periodic one. The constructions rely on the knowledge of weak Lyapunov functionals for the nonlinear source term. The strict Lyapunov functionals are used to prove asymptotic stability in the framework of an appropriate topology. Moreover, when an uncertainty is considered, our construction of a strict Lyapunov functional makes it possible to establish some robustness properties of Input-to-State Stability (ISS) type.

1 :	DISCO (INRIA Saclay - Ile de France)
	INRIA – SUPELEC – CNRS : UMR8506
2 :	Grenoble Images Parole Signal Automatique (GIPSA-lab)
	CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

Équipe de recherche : Division Systèmes

Domaine

:

Sciences de l'ingénieur/Automatique / Robotique

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Contributeur : Christophe Prieur <>

Soumis le : Lundi 28 Mars 2011, 04:45:26

Dernière modification le : Vendredi 10 Juin 2011, 14:36:21