Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable

TL;DR

This paper extends the concept of relative generic controllability and stabilizability from general differential-algebraic equations to port-Hamiltonian systems, providing new dimension-based characterizations.

Contribution

It introduces new results on relative generic controllability and stabilizability specifically for port-Hamiltonian descriptor systems, expanding previous unstructured results.

Findings

Port-Hamiltonian systems are relatively generically controllable.

Port-Hamiltonian systems are relatively generically stabilizable.

Characterizations are based on system dimensions.

Abstract

The present work is a successor of [Ilchmann, Kirchhoff 2022] on generic controllability and of [Ilchmann, Kirchhoff 2023] on relative generic controllability of linear differential-algebraic equations. We extend the result from general, unstructured differential-algebraic equations to differential-algebraic equations of port-Hamiltonian type. We derive new results on relative genericity. These findings are the basis for characterizing relative generic controllability of port-Hamiltonian systems in terms of dimensions. A similar result is proved for relative generic stabilizability.