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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.
The method of analyzing the stability of continuous affine fuzzy system based on fuzzy Lyapunov function is studied.Firstly, the part of the latter part of the fuzzy system is extended to facilitate the stability analysis of homogeneous fuzzy model.And then, The stability conditions of the public Lyapunov function and the fuzzy Lyapunov function are improved, which can be expressed as a set of linear matrix inequalities. The comparison of the obtained stability conditions shows that the stability conditions based on the fuzzy Lyapunov function are the same as those based on the improved common Lyapunov Function is less conservative than the stable condition obtained after the extension of the part.Although the method of stability proof is simpler, , In order to increase the application range of fuzzy Lyapunov function, a method of partitioning fuzzy space is proposed. This method can analyze the stability of the fuzzy system whose membership function is triangular or trapezoidal. The system based on piecewise fuzzy Lyapunov function The stability of the proposed method is validated by an example.