Exponential Stability and Tuning for a Class of Mechanical Systems

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 a passivity-based control technique, namely, PID passivity-based control. We implement such a control approach to stabilize a three-degree-of-freedom robotic arm at the desired equilibrium point to illustrate the mentioned analysis.