3HAB8927-30模块备件使用配置教程

基于李亚普诺夫直接方法，许多学者讨论了离散时间和连续时间模糊控制系统的稳定性分析和设计［37－44］。其中，Tanaka和Sano将［43］中的基本稳定性条件推广到SISO系统的(非)鲁棒稳定性条件，稳定性判据变为从一组李亚普诺夫不等式中寻找一个共同的李亚普诺夫函数问题［44］，由于没有一般的有效方法来解析地寻找一个公共李亚普诺夫函数，故Tanaka等人［43，44］都没有提供寻找李亚普诺夫稳定性条件的公共矩阵P的方法。为解决这一问题，文献［45－47］提出用线性矩阵不等式描述稳定性条件，还有一些学者用一组P矩阵代替文献［43，44］中李亚普诺夫函数的一个公共矩阵P，构造一个逐段近似平滑的二次型李亚普诺夫函数，用于稳定性分析［37］。每一个矩阵P仅对应一个子系统，并表明当且仅当一组合适的Riccati等式有正定对称解，且能得到这些解时，模糊控制系统才是全局稳定的。
使用李亚普诺夫线性化方法，Ying建立了包括非线性对象的TS模糊控制系统局部稳定性的必要和充分条件［23］。另外，一种在大系统中使用的向量李亚普诺夫直接方法，被用于推导多变量模糊系统的稳定性条件［48］；李亚普诺夫第二方法被用于判别模糊系统量化因子选择的稳定性［49］；波波夫-李亚普诺夫方法被用于研究模糊控制系统的鲁棒稳定性［50］。Based on Lyapunov direct method, many scholars have discussed the stability analysis and design of discrete-time and continuous time fuzzy control systems [37-44]. Among them, Tanaka and Sano extended the basic stability condition in [43] to the (non) robust stability condition of SISO system. The stability criterion becomes the problem of finding a common Lyapunov function from a set of Lyapunov inequalities [44]. Since there is no general effective method to analytically find a common Lyapunov function, Therefore, Tanaka et al. [43, 44] did not provide a method to find the common matrix P of Lyapunov stability condition. In order to solve this problem, literature [45-47] proposes to use linear matrix inequality to describe the stability condition. Some scholars use a set of P matrices to replace a common matrix P of Lyapunov function in literature [43,44], and construct a piecewise approximately smooth quadratic Lyapunov function for stability analysis [37]. Each matrix P corresponds to only one subsystem, and shows that the fuzzy control system is globally stable if and only if a set of appropriate Riccati equations have positive definite symmetric solutions and these solutions can be obtained.
Using Lyapunov linearization method, Ying established the necessary and sufficient conditions for the local stability of TS fuzzy control system including nonlinear objects [23]. In addition, a vector Lyapunov direct method used in large-scale systems is used to derive the stability conditions of multivariable fuzzy systems [48]; Lyapunov's second method is used to judge the stability of quantitative factor selection of fuzzy system [49]; Popov Lyapunov method is used to study the robust stability of fuzzy control systems [50].