We study the robustness of the inverse perturbation solution in discrete-time systems modeled by homogeneous Markov chains. We cast the optimal inverse perturbation control as a strictly convex optimization problem, which admits a unique global solution. We show that the optimal inverse perturbation control is robust to estimation errors in the original network. The derived results are applied to the Human melanoma gene regulatory network, where the aim is to force the network to converge to a desired steady-state distribution of gene regulation. © 2011 IEEE.