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This paper addresses the disturbance decoupling problem (DDP) for nonlinear systems, extending the results for continuous-time systems into the discrete-time case. Sufficient conditions are given for the solvability of the problem. The notion of the rank of a one-form is used to find the static measurement feedback that solves the DDP whenever possible. Moreover, necessary and sufficient conditions are given for single-input single-output systems, as well as for multi-input multi-output systems under the additional assumption.

Disturbance decoupling of multi-input multi-output discrete-time nonlinear systems by static measurement feedback