Boundary triplets for skew-symmetric operators and the generation of strongly continuous semigroups

TL;DR

This paper presents a streamlined generation theorem for C0-semigroups using boundary triplets, with applications to port-Hamiltonian systems in stability and control, requiring only basic operator and semigroup theory knowledge.

Contribution

It introduces a self-contained, simplified approach to the generation theorem for C0-semigroups via boundary triplets, with applications to port-Hamiltonian systems.

Findings

Provides a streamlined proof of the generation theorem

Applies the theorem to port-Hamiltonian systems

Discusses stability and control results in detail

Abstract

We give a self-contained and streamlined exposition of a generation theorem for C0-semigroups based on the method of boundary triplets. We apply this theorem to port-Hamiltonian systems where we discuss recent results appearing in stability and control theory. We give detailed proofs and require only a basic knowledge of operator and semigroup theory.