On a class of block operator matrices in system theory

TL;DR

This paper studies a specific class of block operator matrices in system theory, showing they are a subset of known matrices characterized by boundary relations, with applications in scattering passive systems and boundary control.

Contribution

It identifies a subclass of block operator matrices in system theory as a special case of those characterized by boundary relations, linking system theory with maximal monotone operator theory.

Findings

Block operator matrices are a subclass of those characterized by boundary relations.

These matrices are relevant in scattering passive systems and boundary control.

The paper establishes a theoretical connection between system matrices and boundary relations.

Abstract

We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator matrices considered in [Trostorff: A characterization of boundary conditions yielding maximal monotone operators. J. Funct. Anal., 267(8): 2787--2822, 2014], which can be characterized in terms of an associated boundary relation.