Immersion of discrete-time nonlinear system by regular dynamic state feedback into a linear system

Necessary and sufficient conditions for local solvability of the title problem around a given trajectory are obtained. The proposed conditions are less restrictive than those obtained by Lee and Marcus for the problem of immersion a nonlinear system into a linear system via static state feedback. Instrumental in the problem solution is the inversion (structure) algorithm for a discrete-time nonlinear system. The solvability conditions are expressed in terms of the inversion algorithm. Moreover, the construction of both the dynamic state feedback and the immersion map relies on this algorithm Finally, it is shown that, for locally right-invertible systems, the considered problem, unlike the problem of immersion via static state feedback, is always solvable.