Discussion on the paper “ Energy shaping of port - Hamiltonian systems by using alternate passive input - output pairs ” by A . Venkatraman and A . van der Schaft

The paper further elaborates on a passive output that was constructed in [3] with the purpose of providing an energy-balance (EB) interpretation for basic interconnection and damping assignment (BIDA [6, 7]). Such output has its roots in power shaping [4], an alternative method to stabilize nonlinear RLC circuits subjected to the dissipation obstacle [6]. It has been recently shown in [5] that this particular output is also useful in the context of control by interconnection (CbI [8, 6]). The output constructed by swapping the damping (also called the power shaping output) is without doubt worth investigating, as it plays an important role in a somewhat convoluted interplay between: energy-balance, interconnection and damping assignment, control by interconnection and the dissipation obstacle (see [5] for details). Venkatraman and van der Schaft study the power shaping output and its connection to the set of achievable Casimir functions from the more general perspective of Dirac structures [2]. Among other things, the authors show that the process of generating new passive outputs can be understood as a ‘decomposition’ and further ‘re-composition’ of the plant’s Dirac and resistive underlying structures.