Sahiba Arora, Alexander A. Wierzba · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27138 · cited by 0 works (OpenAlex) · open-access PDF
O estudo da estabilidade de saída limitada de entrada limitada (BIBO) de sistemas de dimensão infinita dá origem a dificuldades que não ocorrem na configuração finita-dimensional clássica. Neste artigo, resolvemos várias questões sobre a definição e caracterização da estabilidade BIBO no quadro dos nós do sistema. Em particular, mostramos que a estabilidade $\mathrm C^\infty$-BIBO não precisa implicar a estabilidade $L^\infty$-BIBO em geral, mas que os dois conceitos são equivalentes quando o espaço de saída é reflexivo. Além disso, investigamos o que os resultados clássicos extensivos estendem para a configuração infinita-dimensional, incluindo a relação entre a estabilidade BIBO e a estabilidade exponencial sob pressupostos de controlabilidade
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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