# A Lyapunov Approach to Robust Regulation of Distributed Port-Hamiltonian Systems

## TL;DR

This paper develops a Lyapunov-based control method for robust output regulation of boundary-controlled port-Hamiltonian systems, including complex PDE models, without requiring external well-posedness assumptions, demonstrated on a piezo-actuated tube.

## Contribution

It introduces a Lyapunov approach for robust regulation of port-Hamiltonian systems without external well-posedness assumptions, extending control techniques to complex PDE models.

## Key findings

- Successful robust tracking of a piezo-actuated tube
- No assumptions on external well-posedness needed
- Applicable to second-order PDE models like Euler-Bernoulli beam

## Abstract

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using the internal model principle and the stability analysis using a Lyapunov approach. Contrary to existing works on the same topic no assumption is made on the external well-posedness of the considered class of PDEs. The results are applied to robust tracking of a piezo actuated tube used in atomic force imaging.