  We investigate the asymptotic properties of the trajectories generated by a
second-order dynamical system of proximal-gradient type stated in connection
with the minimization of the sum of a nonsmooth convex and a (possibly
nonconvex) smooth function. The convergence of the generated trajectory to a
critical point of the objective is ensured provided a regularization of the
objective function satisfies the Kurdyka-\L{}ojasiewicz property. We also
provide convergence rates for the trajectory formulated in terms of the
\L{}ojasiewicz exponent.
