  In this paper, we prove the exponential stability property of a class of
mechanical systems represented in the port-Hamiltonian framework. To this end,
we propose a Lyapunov candidate function different from the Hamiltonian of the
system. Moreover, we study how the proposed analysis can be used to determine
the exponential stability and the rate of convergence of some
(nonlinear)-mechanical systems stabilized by two passivity-based control
techniques, namely, PID passivity-based control and interconnection and damping
assignment. We implement the former control approach to stabilize a three
degrees-of-freedom robotic arm at the desired equilibrium point to illustrate
the mentioned analysis.
