Discussion on: On Preserving Passivity in Sampled-data Linear Systems

The goal of this paper is to introduce a methodology to preserve the passivity of a continuous time system under discretization. The authors define a new output that allows to preserve the passivity of the continuous system in its discrete counterpart with the same storage function. First the authors give a general definition of the output and then they specialize it for linear systems. The result proposed in the first part of the paper is very interesting and very general. The authors, generalizing the original work done in [6], consider dynamical systems whose passivity is preserved without adding any external action (e.g. damping as in [4], [2]) but simply recognizing that it is necessary to define a new discrete output. This approach is similar in the spirit to the one proposed in [6] but it is more general since in the paper by Costa-Castelló and Fossas there is no restriction on the structure of the dynamical systems to be sampled while in [6] the authors focuses on port-Hamiltonian systems since their interest was mainly on the interactive control of robotic systems. In the second part of the paper the authors specialize the general result obtained in the first part to linear systems. This part is less interesting than the first one since the results reported in Sec.4 can be easily derived directly from Eq.(11) and the authors go too much into the mathematical details. The LMI analysis doesn’t provide many more information than what is proposed in Sec. 4.1, Proposition 4 is just another way to prove that choosing the output reported in Eq.(11) allows to preserve passivity under sampling. We do not see any meaningful characterization here. In summary, we believe that the result provided in Sec. 3 is of great interest for the control community but that the authors should have worked on an example of digital passivity based control rather than on such a too detailed extension of the result to the linear case.