BIBO stability in infinite dimensions: extensions and limitations of finite-dimensional theory

Sahiba Arora, Alexander A. Wierzba · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27138 · open-access PDF

Abstract

The study of bounded-input bounded-output (BIBO) stability of infinite-dimensional systems gives rise to difficulties that do not occur in the classical finite-dimensional setting. In this paper, we resolve several questions concerning the definition and characterisation of BIBO stability in the framework of system nodes. In particular, we show that $\mathrm C^\infty$-BIBO stability need not imply $L^\infty$-BIBO stability in general, but that the two notions are equivalent when the output space is reflexive. Furthermore, we investigate to what extent classical results extend to the infinite-d

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