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The objective of this paper is to investigate a low complexity method for controlling systems with binary inputs that have costs related to switching. The control objective for this type of systems is often a trade off between the deviation from the reference and the number of switches (weariness energy efficiency etc.). For such systems a steady state solution might never be attained, but rather the optimal behavior might be constituted by a limit cycle. In this paper we consider the problem of finding and controlling the system towards an optimal limit cycle. A low complexity approach giving a suboptimal solution, and avoiding the above problems will be proposed.