An LLC resonant converter has wide application in aerospace, but it is easy for its inherent nonlinear characteristics and small ripple output problem to cause system instability. To accurately describe these problems of the LLC, this paper introduces the generalized state space averaging (GSSA) theory to model the LLC resonant converter system. It transforms the time-domain nonlinear state space model into a GSSA model, and derives the small-signal model of the closed-loop system based on GSSA theory. From eigenvalue analysis and Nyquist curve theory, the effects of component and control parameters and parameter coupling are determined for stability analysis for the LLC resonant converter system. The model and theoretical analysis are verified by simulation. The results of simulation show that the GSSA model has higher accuracy, and can take into account the small ripple factor in the system. Theoretical analysis result and simulation verification result for stability are consistent.