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This paper presents another application of the results in, where existence of the maximizing measure over the total variation distance constraint is established, while the maximizing pay-off is shown to be equivalent to an optimization of a pay-off which is a linear combination of L1 and L∞ norms. Here emphasis is geared towards to uncertain discrete-time controlled stochastic dynamical system, in which the control seeks to minimize the pay-off while the measure seeks to maximize it over a class of measures described by a ball with respect to the total variation distance centered at a nominal measure. Two types of uncertain classes are considered; an uncertainty on the joint distribution, an uncertainty on the conditional distribution. The solution of the minimax problem is investigated via dynamic programming.