Canonical interconnection of discrete linear port-Hamiltonian systems

This paper deals with the canonical interconnection of discrete-time linear port-Hamiltonian systems. A conservative discrete linear port-Hamiltonian dynamics involving a modified conjugate port-output is introduced. It is shown that the projection yielding the discrete dynamics and the composition by canonical interconnection commute. As a by-product, symplecticity of the numerical flow is preserved by interconnection whenever input vector fields are Hamiltonian vector fields, which is analogous to the continuous case. The negative feedback interconnection of two circuits illustrates the results.