Sahiba Arora, Alexander A. Wierzba · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27138 · cited by 0 works (OpenAlex) · open-access PDF
무한 차원 시스템의 한계 입력 한계 출력 (BIBO) 안정성 연구는 고전적인 유한 차원 설정에서 발생하지 않는 어려움을 초래합니다. 이 논문에서는 시스템 노드 프레임에서 BIBO 안정성의 정의 및 특성화에 관한 몇 가지 질문을 해결합니다. 특히 $\mathrm C^\infty$-BIBO 안정성은 일반적으로 $L^\infty$-BIBO 안정성을 의미할 필요가 없지만 출력 공간이 반사적일 때 두 개념이 동등하다는 것을 보여줍니다.
Machine translation (Meta M2M100); the English original follows.
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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