An SVD-like Decomposition of Bounded-Input Bounded-Output Functions

Autor:	Brown, Brian Charles, King, Michael, Warnick, Sean, Yeung, Enoch, Grimsman, David
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: Submitted to the 2024 Conference on Decision and Control
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.00112 Zobrazit plný text záznamu View this record from Arxiv