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- W4287712900 abstract "We use the theory of bialgebras to provide the algebraic background for state space realization theorems for input-output maps of control systems. This allows us to consider from a common viewpoint classical results about formal state space realizations of nonlinear systems and more recent results involving analysis related to families of trees. If $H$ is a bialgebra, we say that $p in H^*$ is differentially produced by the algebra $R$ with the augmentation $epsilon$ if there is right $H$-module algebra structure on $R$ and there exists $f in R$ satisfying $p(h) = epsilon(f cdot h)$. We characterize those $p in H^*$ which are differentially produced." @default.
- W4287712900 created "2022-07-26" @default.
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- W4287712900 date "2020-07-18" @default.
- W4287712900 modified "2023-10-14" @default.
- W4287712900 title "The realization of input-output maps using bialgebras" @default.
- W4287712900 doi "https://doi.org/10.48550/arxiv.2007.09526" @default.
- W4287712900 hasPublicationYear "2020" @default.
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