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In this paper we design discrete port-Hamiltonian systems systematically intwo different ways, by applying discrete gradient methods and splitting methodsrespectively. The discrete port-Hamiltonian systems we get satisfy a discretenotion of passivity, which lets us, by choosing the input appropriately, makethem globally asymptotically stable with respect to an equilibrium point. Wetest methods designed using the discrete gradient approach in numericalexperiments, and the results are encouraging when compared to relevant existingintegrators of identical order.

Energy-Preserving and Passivity-Consistent Numerical Discretization of Port-Hamiltonian Systems