Newest papers

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

Sahiba Arora, Alexander A. Wierzba · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27138 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

無限次元システムの限界入力限界出力(BIBO)安定性の研究は、古典的な限界次元設定では発生しない困難を引き起こします。この論文では、システムノードの枠組みにおけるBIBO安定性の定義と特徴化に関するいくつかの問題を解決します。 特に、 $\mathrm C^\infty$-BIBO安定性は一般的にL^\infty$-BIBO安定性を意味する必要はありませんが、出力スペースが反射性である場合の両方の概念が同等であることを示します。 さらに、我々は、制御性と観測可能性の仮定の下でBIBO安定性と指数的安定性の関係を含む無限次元設定に拡大する古典的な結果

Machine translation (Meta M2M100); the English original follows.

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-dimensional setting, including the relation between BIBO stability and exponential stability under controllability and observability assumptions.

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Topics: BIBO stability, Observability, Stability (learning theory), Controllability, Mathematics, Control theory (sociology)

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