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

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.

26 pages

Cited by in corpus (3)

• Limit-case admissibility for positive infinite-dimensional systems
• Stability of abstract coupled systems
• Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials