Stabilization of port-Hamiltonian systems with discontinuous energy densities

TL;DR

This paper proves exponential stabilization for linear port-Hamiltonian systems with discontinuous energy densities, extending previous results to systems like vibrating strings or beams with jumps in physical properties.

Contribution

It introduces stabilization results for systems with energy densities of bounded variation, including cases with jumps in mass density and elasticity modulus.

Findings

Exponential stabilization achieved for systems with discontinuous energy densities.

Applicable to vibrating strings and beams with jumps in physical parameters.

Extends prior stabilization results to more general, discontinuous cases.

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 modulus of elasticity.