Asymptotic gain results for attractors of semilinear systems

TL;DR

This paper derives asymptotic gain and input-to-state stability results for disturbed semilinear systems, demonstrating their applicability to nonlinear reaction-diffusion equations like the Chaffee-Infante model.

Contribution

It introduces new asymptotic gain and stability results for semilinear systems with disturbances, extending understanding of their attractors.

Findings

Established asymptotic gain along attractors

Proved input-to-state practical stability

Applied results to nonlinear reaction-diffusion equations

Abstract

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee--Infante equations, for example.