Stabilization of port-Hamiltonian systems with discontinuous energy densities

Jochen Schmid

doi:10.3934/eect.2021063

Article Contents

2022, Volume 11, Issue 5: 1775-1795. Doi: 10.3934/eect.2021063

This issue Previous Article Next Article Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Stabilization of port-Hamiltonian systems with discontinuous energy densities

Jochen Schmid

Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany

Received: October 2018

Revised: October 2021

Early access: January 2022

Published: October 2022

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Abstract

We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of bounded variation. In particular, and in contrast to the previously known stabilization results, our result applies to vibrating strings or beams with jumps in their mass density and their modulus of elasticity.

Keywords:

Stabilization of port-Hamiltonian systems,
exponential stability,
energy densities of bounded variation,
static linear boundary control.

Mathematics Subject Classification: 93D15, 93C20, 35L65.

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