In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of L¹-to-L¹ input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output spaces, both are equivalent and preserved under duality transformations. In the general case, neither of these properties is satisfied, but BIBO and LILO stability remain dual to each other.
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Schwenninger et al. (2024) studied this question.
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