, Vadim Kaparin , Ülle Kotta , Tanel Mullari , Maris Tõnso The paper addresses the problem of transforming multi-input multi-output discrete-time nonlinear state equations into the classical observer form using state transformation. Necessary and sufficient geometric solvability conditions are given in terms of vector fields. The results obtained generalize the previous ones in several aspects. First, the results are also applicable to non-reversible systems. Second, they hold almost everywhere, not only around the equilibrium point of the system. The generalizations are possible due to the use of different mathematical tools. The proof of sufficiency also provides a method for finding the state transformation. The results are illustrated by two examples.
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