Attractivity theory for second order non-smooth dynamical systems with application to dry friction

Samir Adly (1)

1 DMI

In this paper, we study the attractivity properties of the set of stationary solutions for a general class of second order non-smooth dynamical system involving friction term. Sufficient conditions for the local attractivity of the set of stationary solutions are given in the case of dry friction and negative viscous damping. An estimation of the attraction domain is also given in this case. Applications can be found in unilateral mechanics.

Mots clés: Variational inequalities; Unilateral dynamical systems; Non-smooth mechanics; Lyapunov stability; LaSalle invariance principle; Convex analysis; Friction problems in mechanics

Domaines: Mathématiques [math]

Samir Adly. Attractivity theory for second order non-smooth dynamical systems with application to dry friction. Journal of Mathematical Analysis and Applications, 2006, 322 (2), pp.1055-1070. ⟨10.1016/j.jmaa.2005.09.076⟩. ⟨hal-00450953⟩