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An approach to the analysis and synthesis of adaptive control systems taking into account the effect of inexact measurements is presented here. The approach is based on the method of generalized quantized compensation. The mathematical tools needed for the analysis are adapted from the discipline of statistical inference. In particular, decision theory is used. An important consequence of inexact measurement is that the problems of identification and of control cannot be considered separately. Decision theory is used as the link that logically relates the two. Current application of decision functions has mostly been limited to cases where the unknown parameters to be determined can take on only discrete values. In view of the continuous variation of the parameters, assumptions that they take on discrete values lead to results whose optimality is not justifiable. Several possible extensions are presented. In addition, a sequential decision scheme that can be applied to reduce expected measurement time is presented. An attempt is made to make the statistical analysis largely self-contained and lucid to those not familiar with statistical inference procedures.