Observability for port-Hamiltonian systems

TL;DR

This paper investigates the observability properties of linear first-order port-Hamiltonian systems, especially when internal energy dissipation occurs, establishing approximate observability via the Hautus test.

Contribution

It extends the understanding of observability in port-Hamiltonian systems to cases with internal dissipation, showing Hautus test satisfaction and approximate observability.

Findings

Hautus test is satisfied for these systems.

Exact observability is not achieved with dissipation.

Systems are approximately observable.

Abstract

The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infinite-dimensional case. In this paper we study a subclass of linear first order port-Hamiltonian systems. These systems are exactly observable when the energy is not dissipated internally and when sufficient observations are made at the boundary. In this article we study the observability properties for these systems when internal dissipation of energy is possible. We cannot show the exact observability, but we do show that the Hautus test is satisfied. In general, the Hautus test is weaker than exact observability, but stronger than approximate observability. Hence we conclude that these systems are approximately observable.