论文标题
使用bialgebras实现输入输出图
The realization of input-output maps using bialgebras
论文作者
论文摘要
我们使用双栅栏理论为控制系统的输入输出图提供了代数背景，以实现状态空间实现定理。这使我们可以从一个共同的观点来考虑有关非线性系统的正式状态空间实现以及涉及与树木家庭有关的分析的最新结果。如果$ h $是bialgebra，我们说$ p \ in h^*$是由代数$ r $差异化的，如果有$ r $的$ h $ h $ -module代数结构，则在$ r $上产生$ε$，并且在r $ p（h）= h）=ε（f（h）=ε（f \ cdot h）中存在$ f \ in $ f \。我们在H^*$中表征了差异产生的$ p \。
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 $ε$ if there is right $H$-module algebra structure on $R$ and there exists $f \in R$ satisfying $p(h) = ε(f \cdot h)$. We characterize those $p \in H^*$ which are differentially produced.
