The paper addresses the invertibility problem for discrete-time nonlinear control systems, described by the input–output equations. The necessary and sufficient conditions for the existence of left and right inverse systems are given. The explicit equations of inverse systems are found by transforming the system equations into the strong Popov form with respect to inputs. The results are obtained under the assumption that the equations are transformable into the strong Popov form using linear equivalence transformations over the field of meromorphic functions.
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