An SVD-like Decomposition of Bounded-Input Bounded-Output Functions
<|reference_start|>An SVD-like Decomposition of Bounded-Input Bounded-Output Functions: The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to SVD, provides an upper bound on the 2-induced norm of bounded-input bounded-output functions, as well as facilitates the computation of generalizations of the notions of row and null spaces. Borrowing from the notion of "lifting" in Koopman operator theory, we construct a finite-dimensional lifting of inputs that relaxes the unitary property of the right-most matrix in traditional SVD, $V^*$, to be an injective, norm-preserving mapping to a slightly higher-dimensional space.<|reference_end|>
@article{brown2024an,
    title={An SVD-like Decomposition of Bounded-Input Bounded-Output Functions},
    author={Brian Charles Brown, Michael King, Sean Warnick, Enoch Yeung, David
  Grimsman},
    journal={arXiv preprint arXiv:2404.00112},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.00112},
    primaryClass={math.OC cs.SY eess.SY}
}