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基于模糊Lyapunov函数的仿射模糊模型稳定性分析

ISSN号：1003-7985
期刊名称：《东南大学学报：英文版》
时间：0
分类：TP183[自动化与计算机技术—控制科学与工程;自动化与计算机技术—控制理论与控制工程]
作者机构：[1]东南大学能源与环境学院,南京210096
相关基金：Specialized Research Fund for the Doctoral Program of Higher Education （ No. 20090092110051）, the Key Project of Chinese Ministry of Education （No. 108060）, the National Natural Science Foundation of China （No. 51076027, 51036002, 51106024）.

关键词：仿射模糊模型, 稳定性分析, 线形矩阵不等式, 模糊LYAPUNOV函数, affine fuzzy system, stability analysis, linear matrix inequalities, fuzzy Lyapunov function

中文摘要：

研究了基于模糊Lyapunov函数分析连续仿射模糊系统稳定性的方法．首先，对模糊系统局部模型的后件部分进行扩展处理，以便于借鉴齐次模糊模型的稳定性分析方法．然后，分别得到基于改进公共Lyapunov函数与模糊Lyapunov函数的系统稳定条件，该条件可表示为一组线性矩阵不等式．通过算例对所得稳定条件进行对比，结果表明：基于模糊Lyapunov函数得到的稳定条件与基于改进公共Lyapunov函数的相比具有较小保守性；对后件部分进行扩展处理后，尽管稳定性证明方法较简便，但与不进行后件处理得到的稳定条件相比，可行解范围有所减小．最后，为了增大模糊Lyapunov函数的应用范围，提出了对模糊空间进行划分的方法，该方法可对隶属度函数为三角形或梯形的模糊系统进行稳定性分析，得到了基于分段模糊Lyapunov函数的系统稳定条件，并通过算例验证了所提方法的有效性．

英文摘要：

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

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