Riesz bases of port-Hamiltonian systems

TL;DR

This paper investigates the spectral properties and Riesz basis conditions of port-Hamiltonian systems, establishing a link between the Riesz basis property and the generation of strongly continuous groups, with implications for spectral structure.

Contribution

It provides a characterization of the Riesz basis property for port-Hamiltonian systems in terms of the system operator generating a strongly continuous group.

Findings

Riesz basis property is equivalent to the operator generating a strongly continuous group.

Spectrum consists solely of eigenvalues in a strip parallel to the imaginary axis.

Eigenvalues can be grouped into finitely many sets with uniform gaps.

Abstract

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap.