Stabilization of oscillators subject to dry friction: Finite time convergence versus exponential decay results

摘要: We investigate the dynamics of an oscillator subject to dry friction via following differential inclusion: (S) x(t) + ∂Φ(x(t)) ∇f(x(t)) ∋0, t ≥ 0, where f: R n → is a smooth potential and Φ: convex function. The modelized by subdifferential term -∂Φ(x). When 0 ∈ int(∂Φ(0)) (dry condition), it was shown Adly, Attouch, Cabot (2006) that unique solution converges in finite time toward equilibrium state.Too provided -∇f(x ∞ ) int(∂Φ(0)). In this paper, we study delicate case vector belongs boundary set ∂Φ(0). prove either or speed convergence exponential. Φ = |.|+b|.| 2 /2, > b obtain existence critical coefficient be below which every stabilizes time. It also geometry ∂Φ(0) plays central role analysis.