Construction of the interconnection and damping structure based on the set of admissible equilibria

In this note, a procedure to apply the interconnection and damping assignment passivity-based control (IDAPBC) methodology with a possibly state-dependent interconnection and damping structure is presented. The imposed structure of closed-loop (port)-controlled Hamiltonian form is motivated by the definition of an equilibrium manifold. We apply our result to passivity-based control of a heat exchanger.