The permanent magnet synchronous wind power generator is investigated, and its mathematical model is established in two-phase synchronous rotating coordinates. By a time scaling transformation and a linear affine transformation, the chaos model is obtained, and the chaos phenomena occur when the model parameters are in a certain range and under running conditions. Then, an uncertain nonlinear model of permanent magnet synchronous wind power generator is established, and a fault observer is designed. When faults occur, the fault observer can estimate the fault quickly and accurately. Simulation results show that the fault observer based on linear matrix inequality approach can diagnosis the fault rapidly and accurately.