Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 70, pp. 1-12.

Title: Energy decay estimates for Lienard's equation with 
       quadratic viscous feedback

Authors: Alexander Y. Khapalov (Washington State Univ., Pullman, WA, USA)
 Parthasarathi Nag (Washington State Univ., Pullman, WA, USA)

Abstract: 
 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.
 
Submitted April 9, 2003. Published June 21, 2003.
Math Subject Classifications: 93D05, 93D15, 93D20.
Key Words: Bilinear systems; stabilization; quadratic feedback; 
           energy decay estimate.