Considering the stability and stabilization of a class of nonlinear fractional order systems, based on the linear matrix inequality(LMI) approach, fractional order T-S fuzzy systems are studied. Using the method of parallel distributed compensation, controllers of fractional order T-S fuzzy systems are designed. Considering the fractional order T-S fuzzy systems with the order α satisfying $0<\alpha<1$, stabilization criterion is given in terms of LMI, which can be solved by Matlab. This criterion can handle the problems of the stability and stabilization of fractional order T-S fuzzy systems which have positive real eigenvalues, while maintaining the consistency with the stability criterion of fractional order systems from Matignon. The limitation and conservatsm of the eigenvalues in negative real parts in the other methods are solved. Numerical simulation results verify the effectiveness of the proposed controller design method.