In this paper, a control of the grid-connected Permanent Magnet Synchronous Generator (PMSG) based on variable speed wind system, taking into account network parameters and the interaction of the wind system with the network is presented. The controlled variables are the speed of the machine and the DC voltage. The proposed Converter Nonlinear Fuzzy Controller (CNFC) is based on a Takagi-Sugeno (TS) fuzzy model and on a control model which allows the electrical system to which the PMSG is connected to be taken into account. Some sufficient conditions for robust stabilization of the TS fuzzy model were derived and have been formulated using a Linear Matrix Inequalities (LMI) format. Obtained performances have been compared with those obtained with Linear Quadratic method (LQ). The control model is a simplified model of the whole system performances which captures the dynamics that are important for the synthesis of the CNFC. The proposed controller methodology is finally demonstrated through the proposed model to illustrate the effectiveness of the proposed method.