In this paper， the author mainly focuses on the influence of non-differential components to power system small signal stability region（SSSR） study. An expressive method is firstly introduced to describe the piecewise， continuous function. It converts the non-differential points into some poles of the derivative function. The left-hand derivative limit and the right-hand derivative limit can be used to approximate the derivatives of such poles according to the requirement. Based on this method and a simple three-bus system， the impact of the exciter limit to power system small signal stability and SSSR is then deeply discussed. It is found that the exciter limit can change elements of the system Jacobian matrix so as to cause jumping of the system critical eigenvalue. New Hopf bifurcation and new oscillation mode can be triggered when exciter voltage hits its limitation. In addition， exciter limit can cause significant topological changes to the power system SSSR. e. g. exciter limit can cause new instability hole in the SSSR and make the region boundaries more complex.