This paper addresses the equivalence under state transformation of a discrete-time nonlinear control system to observer canonical form. Necessary and sufficient conditions for generic equivalence are given for the case when the state equations are not necessarily reversible. The proof is constructive and shows how to find the state transformation if the conditions are satisfied. The derived conditions are then compared with earlier conditions, obtained under more restrictive assumptions, to demonstrate that the earlier result follows directly from our theory. Two examples illustrate the new theory.
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