Switching rule design for a class of switched systems with uncertain equilibrium

This paper addresses the problem of determining the reference and control signals of switching devices, e.g. the duty cycle of electronic valves and converters, in order to drive the system state to a desired value at the equilibrium. For this purpose, the closed loop system is represented as a switched system, where the model of the subsystems are known, and a switching rule (the control) is determined in order to solve the tracking problem. The model of the subsystems are affine and can be obtained by usual identification methods, typically by performing experiments with the system under specific operation conditions associated with the switching devices. The switching rule is determined by solving an LMI problem where a guaranteed cost is minimized and global asymptotic stability of the tracking error dynamics is guaranteed even if sliding motions occur at any switching surface of the system. The potential of the results are illustrated on a true refrigeration system, namely a domestic refrigerator, where the purpose is to control the temperature in two compartments of the refrigerator: the fresh food and the freezer compartments. In this case the control signals to be determined are those associated with the definition of the compressor rotation and the distribution of the refrigeration fluid to the compartments.