Lyapunov stability analysis of a mass-spring system subject to friction

Matthieu Barreau, Sophie Tarbouriech, Frédéric Gouaisbaut

Abstract: Highlights•The stability analysis of mass–spring system subject to a nonlinear friction force is conducted using quadratic Lyapunov functions, leading to stability tests expressed by LMIs.•We give a precise estimation of a global attractor with emphasis on the practical consequences.•If there exists a basin of attraction, we provide an algorithm to give an inner-estimation of the latter.•We mix the two previous results to state the global exponential stability of the system. This work proves then rigorously what was experimentally already noted: for a reference speed large enough, the unique equilibrium point is globally exponentially stable.