On feedback passivation under sampling

TL;DR

This paper demonstrates how feedback passivation properties under sampling can be maintained in digital control by redefining the passifying output map, with applications to port Hamiltonian systems and a gravity pendulum example.

Contribution

It introduces a constructive method to preserve feedback passivation under sampling through a redefined output map depending on the sampling period.

Findings

Feedback passivation can be preserved under sampling with a redefined output map.

The method is applicable to port Hamiltonian dynamics and Interconnection and Damping Assignment feedback.

Performance is validated on a gravity pendulum example.

Abstract

In this paper we show that feedback passivation under sampling can be preserved under digital control through the redefinition of a passifying output map which depends on the sampling period. The design is constructive and approximate solutions make sense. The procedure is applied to port Hamiltonian dynamics and Interconnection and Damping Assignment feedback. Performances are illustrated over the gravity pendulum example.