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An optimization problem for systems that are subject to perturbations where both state observations and control actions are impulsive is here addressed. The dynamics equation is given by a differential inclusion ( ) ( , ( )) x t F t x t ∈ and the optimal strategy is the minimizer of the worst viable perturbation process (minimax). Such formulation is appropriate when noise is barely known but limited and when observing the system, similarly to changing its state, has a positive cost that is not negligible. Since observation and control instants are stopping times relative to the σ-algebra generated by the state values at previous observation instants (which are the only known state values) this formulation has a discrete time analogue, which is exploited. Sufficient conditions for optimality and a derived algorithm are presented. In the presence of a certain type of multifunctions F(t, x(t)), this algorithm provides efficient solutions.