A novel polynomial membership functions based control method for T-S fuzzy systems.

Area of Science:

• Control Engineering
• Fuzzy Systems Theory
• Nonlinear Control

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling nonlinear systems.
• Existing stability analysis methods for T-S fuzzy systems can be conservative.
• State feedback stabilization is crucial for ensuring system performance and safety.

Purpose of the Study:

• To develop a novel stability synthesis method for T-S fuzzy systems.
• To reduce the conservatism in the stability analysis of T-S fuzzy systems.
• To provide less conservative linear matrix inequality (LMI) conditions for stability.

Main Methods:

• Approximation of system membership functions using nonlinear polynomials.
• Polynomial transformation to convert polynomial membership functions into a linear form.
• Stability analysis using a membership function-dependent approach.

Main Results:

• Achieved satisfactory approximation results for membership functions.
• Facilitated the synthesis process with improved approximation precision.
• Derived linear matrix inequality (LMI) based stability conditions.
• Demonstrated conservatism reduction through numerical and practical examples.

Conclusions:

• The proposed method effectively reduces conservatism in T-S fuzzy system stability analysis.
• The polynomial approximation and transformation techniques enhance stability synthesis.
• The findings contribute to more precise and less conservative fuzzy control design.