The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity.

The paper deals with interconnection and damping assignment for discrete-time port-Hamiltonian systems. Based on a novel state representation, suitably shaped to address energybased control design, the nonlinear discrete-time controller is characterized and the solution is explicitly computed in the linear case. The design worked out on the exact sampled-data model of a mechanical system confirms the effectiveness of the controller.

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