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Broadcast control of group of Markov chains

This paper addresses broadcast control for a group of Markov chains. The problem studied here is to find a controller governing multiple Markov chains by observing the group performance and sending the same signal to all the Markov chains indiscriminatingly. As a solution to the problem, we consider here integral-type broadcast controllers and provide a sufficient condition for the controller gain to stabilize the resulting broadcast control system. The result is demonstrated by numerical simulation.