Immersion and immersion by nonsingular feedback of a discrete-time nonlinear system into a linear system

An analytic discrete-time nonlinear system is considered. Necessary and sufficient conditions for immersion of the system into a linear system are given. Local immersion is defined by nonsingular feedback into a linear system and given necessary and sufficient conditions for this problem. It is shown that a similar approach can also be applied to continuous-time affine nonlinear systems.<
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