Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T–S Fuzzy Systems
提出一种基于隶属函数导数极值的方法，通过坐标变换算法将导数形状信息融入稳定性条件，降低T-S模糊系统稳定性分析与综合的保守性，并通过仿真验证效果。
In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.