This paper considers the problem of identifying the parameters of an
uncertain linear system by means of feedback control. The problem is approached
by considering time-varying controllers. It is shown that even when the
uncertainty set is not finite, parameter identifiability can be generically
ensured by switching among a finite number of linear time-invariant
controllers. The results are shown to have several implications, ranging from
fault detection and isolation to adaptive and supervisory control. Practical
aspects of the problem are also discussed in details