Analysis and synthesis of discrete nonlinear passive systems via affine T–S fuzzy models

Abstract

The article considers the analysis and synthesis problem for the discrete nonlinear systems, which are represented by the discrete affine Takagi–Sugeno (T–S) fuzzy models. The state feedback fuzzy controller design methodology is developed to guarantee that the affine T–S fuzzy models achieve Lyapunov stability and strict input passivity. In order to find a suitable fuzzy controller, an Iterative Linear Matrix Inequality (ILMI) algorithm is employed in this article to solve the stability conditions for the closed-loop affine T–S fuzzy models. Finally, the application of the proposed fuzzy controller design methodology is manifested via a numerical example with computer simulations.

Keywords:

• affine Takagi–Sugeno fuzzy model
• passive systems
• S-procedure
• iterative linear matrix inequality

Acknowledgements

The authors would like, to express their sincere gratitude to anonymous reviewers, who gave us some constructive comments, criticisms and suggestions. This work was supported by the National Science Council of the Republic of China under Contract NSC94-2213-E-019-006.