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

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.

Automated summary

In this paper, an improved piecewise membership functions dependent approach is proposed for the stability analysis issue of a T-S fuzzy system to reduce conservatism. A series of decoupled polynomial functions are approximated to represent the nonlinear membership functions based on a least-square method. Furthermore, a newly proposed derivative-integral nonuniform division approach is adopted to select the piecewise vertices. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, the effectiveness of the designed method is illustrated through a mass-spring-damper (MSD) simulation example.