Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type

TL;DR

This paper develops a theoretical framework for analyzing the well-posedness and stability of interconnected networks of infinite-dimensional port-Hamiltonian systems with varying orders, extending existing results to more complex network configurations.

Contribution

It generalizes well-posedness and stability results from single port-Hamiltonian systems to networks with diverse orders and boundary interconnections.

Findings

Established well-posedness for interconnected port-Hamiltonian networks.

Proved stability results for these networks.

Applied theory to specific model examples.

Abstract

We consider networks of infinite-dimensional port-Hamiltonian systems $\mathfrak{S}_i$ on one-dimensional spatial domains. These subsystems of port-Hamiltonian type are interconnected via boundary control and observation and are allowed to be of distinct port-Hamiltonian orders $N_i \in \mathbb{N}$. Wellposedness and stability results for port-Hamiltonian systems of fixed order $N \in \mathbb{N}$ are thereby generalised to networks of such. The abstract theory is applied to some particular model examples.