Interconnection and damping assignment passivity-based control for port-Hamiltonian mechanical systems with only position measurements

A dynamic extension for position feedback of port-Hamiltonian mechanical systems is studied. First we look at the consequences for the matching equations when applying Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Then we look at the possibilities of asymptotically stabilizing a class of port-Hamiltonian mechanical systems without having to know the velocities, as once presented for Euler-Lagrange (EL) systems. Here it is shown how the idea of damping injection by dynamic extension works when shaping the total energy in the port-Hamiltonian framework