Dissipativity-Preserving Model Reduction for Takagi–Sugeno Fuzzy Systems

摘要

This paper is concerned with the dissipativity-preserving model reduction problem for Takagi-Sugeno (T-S) fuzzy systems. The principal goal is to approximate the high-order T-S model with a dissipative reduced-order T-S model. The number of fuzzy rules and the membership functions of the reduced-order T-S model are chosen freely to enhance design flexibility. To this end, an H-infinity performance index is used to describe the approximation error. Meanwhile, dissipativity of the reduced-order model is guaranteed by satisfying a dissipation inequality. With the aid of fuzzy-basis-dependent Lyapunov functions and slack variable techniques, less conservative design conditions for reduced-order models are derived. An algorithm is proposed to calculate a desired reduced-order model. A rail traction control system is given to illustrate the effectiveness of the proposed method and the advantages over the existing methods.