Nonuniform piecewise membership function approximation methods based robust tracking control design of T‐S fuzzy systems

• Published in: International journal of robust and nonlinear control Vol. 32; no. 8; pp. 4980 - 5001
• Main Authors: Xie, Wen‐Bo, Xu, Bo‐Lin, Peng, Chen, Zhang, Jian
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2022
• Subjects: Apexes; Approximation; conservatism; Control tasks; Derivatives; Functions (mathematics); Fuzzy systems; Integrals; Mathematical analysis; Polynomials; Robust control; Stability analysis; Takagi‐Sugeno fuzzy systems; Tracking control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6072

For the stability analysis issue of a T‐S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least‐square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise vertices are chosen by a newly proposed derivative‐integral nonuniform division approach. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, a mass‐spring‐damper (MSD) simulation example is adopted to illustrate the effectiveness of the designed method.