基于连续时间 T-S 模糊模型非线性系统的稳定性分析

摘要

A novel stability analyisis method was proposed for addressing the problem of stability analysis of continuous-time nonlinear systems based on the Takagi-Sugeno fuzzy model.In the process of stability analysis,a slack matrix method was applied to further considering the useful underlying fuzzy membership functions’time derivative.Owing to more freedom can be introduced in virtue of the slack matrix method,the obtained stability criteria are less conservative than those existing ones. Furthermore,the stability criteria proposed are given in terms of linear matrix inequality,which is easily solved via MATLAB numerical software.Finally,a numerical example was given to illustrate the effectiveness of the proposed result.%针对一类连续时间非线性系统的稳定性分析问题，提出一种基于 Takagi-Sugeno 模糊模型的稳定性分析新方法。在模糊系统稳定性分析过程中，通过加入松弛矩阵技术，能充分考虑模糊隶属函数时间导数的有用信息，并显著增加稳定性分析的自由度，从而获得比已有稳定性判据保守性更小的连续时间 Takagi-Sugeno 模糊系统稳定性判据。所提出的稳定性判据以线性矩阵不等式形式给出，可方便地通过 MATLAB 数值软件求解。仿真实验验证了所提方法的有效性。