Energy-Preserving and Passivity-Consistent Numerical Discretization of Port-Hamiltonian Systems
For researchers working on structure-preserving numerical integration of port-Hamiltonian systems, this provides new discretization methods that guarantee passivity and stability.
The paper develops two systematic approaches (discrete gradient and splitting methods) to discretize port-Hamiltonian systems while preserving energy and passivity, achieving global asymptotic stability. Numerical experiments show encouraging results compared to existing integrators of the same order.
In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion of passivity, which lets us, by choosing the input appropriately, make them globally asymptotically stable with respect to an equilibrium point. We test methods designed using the discrete gradient approach in numerical experiments, and the results are encouraging when compared to relevant existing integrators of identical order.