Alternative Passive Maps for Infinite-Dimensional Systems Using Mixed-Potential Functions

Abstract

This paper aims at developing a Brayton-Moser analogue of an infinite-dimensional system in the port-Hamiltonian framework, defined with respect to a Stokes-Dirac structure. It is shown that such a formulation leads to defining alternative passive maps, which differ from those in the port-Hamiltonian framework via a “power-like” function called the mixed-potential function. This mixed-potential function can also be used for stability analysis. We present our results for a general port-Hamiltonian system, with Maxwell's equations and the transmission line, with nonzero boundary conditions, as examples.