Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation

We introduce a family of discrete-time lossless input-state-output port-Hamiltonian systems based on numerical time integration with symplectic collocation schemes. For systems with non-zero input, symplecticity extends to the conservation of a discrete energy balance, based on which a discrete-time Dirac structure is defined. Using Gauss-Legendre collocation, the corresponding quadrature formula allows to quantify the discretization error for the supplied energy. On a linear example, backward error analysis and numerical experiments are performed in order to illustrate the accuracy of the resulting structure-preserving integration schemes. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.