Geodesic
Energy decay estimates for Lienard's equation with quadratic viscous feedback
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the stabilization for a well-known Lienard's system of ordinary differential equations modelling oscillatory phenomena. It is known that such a system is asymptotically stable when a linear viscous (motion-activated) damping with constant gain is engaged. However, in many applications it seems more realistic that the aforementioned gain is not constant and does depend on the deviation from equilibrium. In this article, we consider a (nonlinear) gain, introduced in [2], which is proportional to the square of such deviation and derive an explicit energy decay estimate for solutions of the corresponding "damped" Lienard's system. We also discuss the place of our result in the framework of stabilization of so-called critical bilinear systems.
Classification : 93D05, 93D15, 93D20
Keywords: bilinear systems, stabilization, quadratic feedback, energy decay estimate 
@article{EJDE_2003__2003__a32,
     author = {Khapalov, Alexander Y. and Nag, Parthasarathi},
     title = {Energy decay estimates for {Lienard's} equation with quadratic viscous feedback},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a32/}
}
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Khapalov, Alexander Y.; Nag, Parthasarathi. Energy decay estimates for Lienard's equation with quadratic viscous feedback. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a32/