Abstract: The stability of TEA is a very important problem in the space station TEA maintaining control study.The Lyapunov theory is used to judge the stability of TEA by calculating all the characteristic vectors and eigenvalues of the differential operator,and the stability-based LQR controller for space station attitude control is developed based on the linearized attitude dynamic equations.The simulation results prove:(1) the advantages of TEA as a balanced attitude;(2) the effectiveness of the stability judge method of calculating all the characteristic vectors and eigenvalues of the differential operator.