On the immersion of a discrete-time polynomial analytic system into a polynomial affine one
Within the class of discrete-time nonlinear systems which are polynomial with respect to the input the following problem is considered. Given a system \(\Sigma\) analytic with respect to the state, does there exist another system \(\Sigma'\) linear with respect to the state and an analytic map \(\tau\) from the state space \(R^ N\) of \(\Sigma\) to the state space \(R^{N'}\) of \(\Sigma\) ' such that for any \(x\in R^ N\) the input-output behavior of \(\Sigma\) initialized at \(x\) coincides with the input-output behaviour of \(\Sigma'\) initialized at \(x'=\tau (x)\). The authors give necessary and sufficient conditions on \(\Sigma\) for the existence of such \(\Sigma'\) and \(\tau\).
scientific article; zbMATH DE number 3882277
scientific article