  This paper deals with the stability analysis of a mass-spring system subject
to friction using Lyapunov-based arguments. As the described system presents a
stick-slip phenomenon, the mass may then periodically sticks to the ground. The
objective consists of developing numerically tractable conditions ensuring the
global asymptotic stability of the unique equilibrium point. The proposed
approach merges two intermediate results: The first one relies on the
characterization of an attractor around the origin, to which converges the
closed-loop trajectories. The second result assesses the regional asymptotic
stability of the equilibrium point by estimating its basin of attraction. The
main result relies on conditions allowing to ensure that the attractor issued
from the first result is included in the basin of attraction of the origin
computed from the second result. An illustrative example draws the interest of
the approach.
