从模糊控制系统稳定性分析的结果可知，一般的方法是李亚普诺夫方法，但比较保守，圆判据则更保守。对于其它一些典型的模糊控制系统稳定性分析方法，要求对象模型确定且应满足一些连续性限制。如描述函数分析极限环，本质上要求一个线性时不变对象或者具有某一特定数学形式的对象，使得非线性在循环中有界于一个非线性元件。
5 结论和展望
通过对模糊控制器结构的解析分析，可以揭示模糊控制器的本质和工作机理，建立模糊控制器与经典控制器之间的关系，而稳定性分析结果可用于指导模糊控制系统的分析和设计。虽然目前已得到许多解析结果，但与经典控制理论相比，解析模糊控制理论显得仍不成熟。许多经典控制理论和概念有待于进一步推广到模糊控制系统的分析和设计：
1)在解析结构分析方面，TS模糊控制器的结构分析需推广到更一般的情况及MIMO控制器；一般Mamdani和TS模糊控制器的极限结构理论需进一步讨论；同时，复杂系统模糊控制的解析理论有待进一步深入。如：分层递阶模糊控制系统可解决多变量模糊控制器的维数灾问题，且已被证明是控制器［72］，因此，有必要对这类控制器的结构进行解析分析。
2)模糊控制稳定性分析结果尚较缺乏。目前的方法多少都受到一些限制，更一般化的稳定性判据，尤其是基于模糊控制器解析结构的易理解且具广泛应用性的方法应加以研究。
3)其它如模糊控制系统的鲁棒性、能观性和能控性等同样有待于深入研究和进一步发展。
4)需开发基于解析理论的模糊系统计算机辅助
设计软件
。鉴于目前许多模糊系统开发软件都缺乏解析能力，我们正在研制一种能用于解析分析、设计和开发模糊系统的软件包。
总之，成熟且丰富的经典控制理论与模糊控制相结合，将有助于更好地分析和设计模糊控制系统，从而奠定模糊控制理论基础，并使21世纪这一人类智能的核心技术更具生命力。
Robust control techniques (such as vector stabilization, H ∞ control theory and linear matrix inequality) are used to derive TS fuzzy control systems with uncertainty [46]. In addition, the concept of generalized energy [65], the concept of cell mapping [66], the geometric state space method [67], the Hurwitz stability condition method [68], the absolute stability criterion method [69], the method based on kudrewicz theory [70] and the extended Haddad method [71] have been used to analyze the stability of fuzzy control systems.From the results of stability analysis of fuzzy control system, the most general method is Lyapunov method, but it is more conservative, and the circular criterion is more conservative. For some other typical fuzzy control system stability analysis methods, the object model is required to be determined and some continuity constraints should be met. For example, the description function analysis limit cycle essentially requires a linear time invariant object or an object with a specific mathematical form, so that the nonlinearity is bounded by a nonlinear element in the cycle.
5 conclusions and Prospects
Through the analytical analysis of the structure of fuzzy controller, the essence and working mechanism of fuzzy controller can be revealed, and the relationship between fuzzy controller and classical controller can be established. The stability analysis results can be used to guide the analysis and design of fuzzy control system. Although many analytical results have been obtained, compared with the classical control theory, the analytical fuzzy control theory is still immature. Many classical control theories and concepts need to be further extended to the analysis and design of fuzzy control system:
1) In terms of analytical structure analysis, the structure analysis of TS fuzzy controller needs to be extended to more general cases and MIMO controller; The limit structure theory of general Mamdani and TS fuzzy controllers needs further discussion; At the same time, the analytical theory of fuzzy control for complex systems needs to be further deepened. For example, hierarchical fuzzy control system can solve the dimension disaster of multivariable fuzzy controller, and has been proved to be a universal controller [72]. Therefore, it is necessary to analyze the structure of this kind of controller.
2) The results of fuzzy control stability analysis are still lacking. The current methods are somewhat limited. More general stability criteria, especially the easy to understand and widely used methods based on the analytical structure of fuzzy controller, should be studied.
3) Others, such as the robustness, observability and controllability of fuzzy control system, also need to be further studied and developed.
4) It is necessary to develop computer-aided design of fuzzy system based on analytical theory
Design software
。 In view of the lack of analytical ability of many fuzzy system development software, we are developing a software package that can be used for analytical analysis, design and development of fuzzy system.
In short, the combination of mature and rich classical control theory and fuzzy control will help to better analyze and design fuzzy control system, so as to lay the theoretical foundation of fuzzy control and make the core technology of human intelligence in the 21st century more vitality.
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