Feedback theory approach to positivity and stability of evolution equations

TL;DR

This paper investigates the positivity and exponential stability of perturbed semigroups using feedback theory, with applications to hyperbolic systems and boundary delays, advancing understanding of stability in infinite-dimensional systems.

Contribution

It introduces a feedback theory approach to analyze positivity and stability of evolution equations, including systems with boundary delays, which is a novel application in this context.

Findings

Established conditions for positivity and exponential stability of perturbed semigroups.

Applied the theoretical results to hyperbolic systems with boundary delays.

Demonstrated the effectiveness of feedback theory in stability analysis of infinite-dimensional systems.

Abstract

In this paper, we study the positivity and (uniform) exponential stability of a large class of perturbed semigroups. Our approach is essentially based on the feedback theory of infinite-dimensional linear systems. The obtained results are applied to the stability of hyperbolic systems including those with a delay at the boundary conditions.