Model Reduction of Interval Type-2 Fuzzy-Model-Based Systems

Abstract

This chapter considers the problem of model reduction for IT2 fuzzy systems subject to $\mathcal {D}$-stability constraints. The membership functions and the number of rules can be freely chosen and they are different between the original system and the reduced-order system. By introducing some slack matrices and utilizing Lyapunov stability theory, the existence condition of model reduction is obtained to guarantee that the reduced-order model can approximate the original system with an $H_{\infty }$ performance. The parameters of the reduced-order system in the condition can be obtained by standard software.