Control Design for Linear Port-Hamiltonian Boundary Control Systems: An Overview

A. Macchelli*, Y. Le Gorrec, H. Ramírez, H. Zwart, F. Califano

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
21 Downloads (Pure)


In this paper, we provide an overview of some control synthesis methodologies for boundary control systems (BCS) in port-Hamiltonian form. At first, it is shown how to design a state-feedback control action able to shape the energy function to move its minimum at the desired equilibrium, and how to achieve asymptotic stability via damping injection. Secondly, general conditions that a linear regulator has to satisfy to have a well-posed and exponentially stable closed-loop system are presented. This second methodology is illustrated with reference to two specific stabilisation scenarios, namely when the plant is in impedance or in scattering form. It is also shown how these techniques can be employed in the analysis of more general systems described by coupled PDEs and ODEs. As an example, the repetitive control scheme is studied, and conditions to have asymptotic tracking of generic periodic reference signals are presented.

Original languageEnglish
Title of host publicationStabilization of Distributed Parameter Systems: Design Methods and Applications
EditorsGrigory Sklyar, Alexander Zuyev
Number of pages16
ISBN (Electronic)978-3-030-61742-4
ISBN (Print)978-3-030-61741-7
Publication statusPublished - 2 Mar 2021
EventInternational Congress on Industrial and Applied Mathematics 2019 - Universitat de València, Valencia, Spain
Duration: 15 Jul 201919 Jul 2019

Publication series

NameSEMA SIMAI Springer Series
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X


ConferenceInternational Congress on Industrial and Applied Mathematics 2019
Abbreviated titleICIAM 2019
Internet address


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