Linear port-Hamiltonian systems are generically controllable

TL;DR

This paper introduces the concept of relative generic subsets and demonstrates that controllability is a typical property in linear port-Hamiltonian systems, meaning most such systems are controllable.

Contribution

It establishes that controllability is a generic property in linear port-Hamiltonian systems using the new concept of relative generic subsets.

Findings

Controllability is almost surely in linear port-Hamiltonian systems.

The set of controllable systems is a relative generic subset.

Most randomly chosen port-Hamiltonian systems are controllable.

Abstract

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian systems. This implies that a random, continuously distributed port-Hamiltonian system is almost surely controllable.