基于变结构系统理论，可以得到控制系统的跟踪精度和模糊控制器的I／O模糊集映射形状之间的关系，从而可以解释模糊控制器的鲁棒性和控制性能。文献［24，56，57］研究了基于变结构控制框架的模糊控制系统的稳定性，通过输出反馈的模糊变结构控制，并用李亚普诺夫方法证明了闭环控制系统是全局有界输入有界输出稳定的［58］。若使用变结构控制类型的模糊规则集，模糊控制器从语义和定量上可显示出变结构的特性。为便于李亚普诺夫稳定性判据能指导设计和调整模糊控制器，文献［30］推导出模糊控制器的具体数学表达式。
Because the fuzzy controller adopts semantic expression, it is difficult to ensure the stability and robustness of the fuzzy control system in the system design. Sliding mode control has an obvious characteristic, that is, it can deal with the nonlinearity of the control system and is robust control. Therefore, some scholars propose to design a fuzzy controller with fuzzy sliding mode surface, so that the stability of closed-loop control system can be proved by Lyapunov theory [25, 27, 51-54]. Palm and driankov used the concept of sliding mode control to analyze the stability and robustness of gain planning closed-loop fuzzy control system [55]. Other scholars use fuzzy reasoning to deal with the nonlinearity of the control system and reduce the control tremor, so that the stability of the control system can be guaranteed based on Lyapunov method [26].Based on the variable structure system theory, the relationship between the tracking accuracy of the control system and the I / O fuzzy set mapping shape of the fuzzy controller can be obtained, which can explain the robustness and control performance of the fuzzy controller. Reference [24, 56, 57] studies the stability of fuzzy control system based on variable structure control framework. Through fuzzy variable structure control with output feedback, it is proved that the closed-loop control system is globally bounded input bounded output stable by Lyapunov method [58]. If the fuzzy rule set of variable structure control type is used, the fuzzy controller can show the characteristics of variable structure semantically and quantitatively. In order that Lyapunov stability criterion can guide the design and adjustment of fuzzy controller, the specific mathematical expression of fuzzy controller is derived in reference [30].
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