Hankel Norm Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems with State Delay

This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T-S) fuzzy systems. Compared with the type-1 T-S fuzzy system, the interval type-2 T-S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T-S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis.