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What is discussed in this article is to find a way for membership functions optimally. In most scholars, these functions are constant and have a limited number. Therefore, in some cases, this limitation reduces control performance improvement. One of the best solutions is finding these functions in a differential form. This article used the Takagi-Sugeno function as a fuzzy detector to identify and control a nonlinear SISO system by direct adaptive reference model control. Using this method with Lyapunov for the stability of the control system makes output fuzzy linguistic variables optimally. Then simultaneously using these values, membership functions can be defined in differential form. Therefore, there is no other limitation in the variance and midpoint.