Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T–S Fuzzy Systems

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.