Direct adaptive fuzzy controllers have been proposed and discussed in the literature. Even though such controllers have been proven to be effective, in our study, some phenomena are observed. In this paper, those problems of using adaptive fuzzy controllers for unknown nonlinear systems are reported. The role of a parameter matrix required in the Lyapunov equation is discussed. It can be found that even though the Lyapunov synthesis approach has already proven that the system is asymptotically stable, the parameter matrix still needs to be selected appropriately beside of the symmetric positive definite property. Another issue is that it can also be found in our simulations that this kind of adaptive fuzzy controllers does not converge to a fixed controller as assumed in the literature, but adaptively adjusts its parameters according to the errors. As a consequence, when the considered system has sensory noise, the system may gradually become unstable. Ways of restraining such an unbounded phenomenon are proposed. From our simulations, the proposed approaches can have nice performance.