Model reduction for interval type-2 Takagi–Sugeno fuzzy systems

This paper investigates the problem of model reduction for interval type-2 (IT2) fuzzy systems subject to 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∞H∞ performance. The parameters of the reduced-order system in the condition can be obtained by standard software. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed results.