The purpose of this study is to analyze the behavior of a set of thermally-controlled rooms arranged in the form of a ring. Each room is heated and can exchange heat with its neighbors as well as with the environment. The heater in each room is PI controlled. A lumped capacitance approximation is used for the rooms leading to a system of first-order differential equations. Numerical methods are used to determine the time-dependent behavior of the coupled system. The linear stability of the system is analyzed for various parameters. The stability is found to be independent of the strength of the thermal coupling between rooms.

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