Abstract: The trajectory eigenvalue method transforms the nonlinear system model into a time-varying linear system model with a disturbing term.The analytical solutions of two examples show that trajectory eigenvalues cannot be used to determine the global stability of time-varying linear systems.For this reason,the extended trajectory eigenvalue analysis is introduced and its effect is validated by a simple system with an e-exponential component.However,the extended trajectory eigenvalue analysis cannot be applied to power systems,because their models are not consistent with the hierarchical equation,and the trajectory eigenvalues cannot be obtained analytically.In fact,all trajectory eigenvalue techniques are faced with the difficulty in determining the global stability of power systems,which can only be solved by the concept of the dynamic saddle point（DSP）.