Dissipativity-Preserving Model Reduction for Takagi–Sugeno Fuzzy Systems

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 <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> 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.