A novel [formula omitted] control for T-S fuzzy systems with transform matching membership functions

Abstract

This article studies H∞ optimization issue of Takagi-Sugeno (T-S) fuzzy systems with an improved transform matching membership functions (MFs) approach. Different from existing transform matching MFs control method, a polynomial disassembling strategy is first proposed for T-S fuzzy systems. Then, combining with parameterized linear matrix inequality (LMI) technique which can remove the inequality constraints between the MFs in systems and fuzzy controllers, sufficient conditions are presented to maintain asymptotic stability and desired H∞ performance for studied plants. Afterwards, a novel MFs online optimization algorithm is proposed for the first time to automatically adjust the values of scaling and bias parameters so as to realize better H∞ performance. In contrast to the traditional control using improved matching MFs, the practical behavior of disturbance attenuation index is reduced efficiently. Additionally, the proposed MFs online optimization algorithm is capable of sustaining the desired H∞ performance when the disturbance channels exist modeling errors, i.e., the practical disturbance attenuation index γ is still less than the preset value. For guaranteeing the convergence of cost function, sufficient condition is obtained based upon Lyapunov stability theory. Finally, two demonstrative simulations are presented to confirm the advantages and benefits of the novel MFs online optimization control strategy.