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In general, interval plants with a large uncertainty can not be robustly stabilized by a linear, time-invariant controller. The solution presented in this paper is in terms of an overall non linear control law given by the connection of a linear, deterministic, time-varying compensator and of a supervisor. The compensator may assume a finite number of possible different configurations, at least one of the which stabilizes the plant. The task of the supervisor is that of determining the switching instants of a scanning among the elements of the family, according to a suitably defined experimental test on the output of the system.