A linear programming approach to the design of thermostat controllers of interconnected thermal systems

We investigate how to tune the thermostat hysteresis for a system of interconnected thermal processes. Using linear programming techniques and the worst-case analysis we compute switch levels for the controller to make the system stay close to the desired temperature levels. Both the cases with and without amplitude bounded disturbances are treated. The same technique can also be applied to a system of interconnected tanks despite the fact that such a system is nonlinear.