Input-to-state stability for parabolic boundary control: Linear and semi-linear systems

TL;DR

This paper reviews input-to-state stability (ISS) for parabolic boundary control systems, covering linear and semi-linear PDEs with respect to various input norms, highlighting recent advances in the field.

Contribution

It extends existing ISS results to semi-linear parabolic equations and considers general $L^{p}$-input norms, broadening the scope of stability analysis for boundary control systems.

Findings

ISS established for linear parabolic boundary control systems.

Extensions of ISS results to semi-linear equations.

Analysis includes general $L^{p}$-input norms.

Abstract

Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects enter the situation. This note reviews input-to-state stability for parabolic equations with respect to general $L^{p}$-input-norms in the linear case and includes extensions of recent results on semilinear equations.