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Internal model control (IMC) is an established technique in continuous-time linear control for SISO an MIMO fully-actuated systems but has not been developed for discrete-time under-actuated systems. In this paper we present a new IMC structure to the multivariable under-actuated systems, which is based on a specific inversion principle of the model plant. Simulated examples are presented to prove the effectiveness of the proposed control method to ensure set-point tracking, stability and disturbance rejection.