The inverted pendulum is a complicated system, which is an ideal platform to carry out all kinds of control theory and teach and check out controlled experiment. According to the concept of characteistic roots' sensitivity, the method of using characteistic roots' sensitivity to analyze the inverted pendulum system is introduced. Then, MATLAB is used to draw the inverted pendulum's root locus, the effect of the gains'changes to sensitivities of the characteristic roots are found. Finally, we can choose appropriated gain and characteistic root to realize required function in the root locus.%倒立摆是一个复杂的非线性系统，是进行各种控制理论教学及验证先进控制理论的理想平台。本文根据特征根灵敏度分析理论，提出了一种倒立摆控制系统特征根的分析与设计方法，利用MATLAB绘制倒立摆控制系统的根轨迹，得到增益变化对特征根灵敏度的影响。最后，通过在根轨迹上选择合适的增益和特征根，满足系统设计的要求。
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