ROBUST LINEAR OUTPUT FEEDBACK CONTROL DESIGN FOR NONLINEAR CHAOTIC SYSTEMS VIA T-S FUZZY MODEL WITH H∞ SETTING

In this paper, the problem of H-infinity control design is studied for a nonlinear chaotic system via its corresponding Takagi-Sugeno (T-S) fuzzy model. It is known that many nonlinear chaotic systems can be exactly represented by their corresponding T-S fuzzy models. First, in this study, the T-S fuzzy model is proposed to represent a class of nonlinear chaotic systems. Next, a linear output feedback control scheme, where only linear controller and linear observer are considered, with H-infinity setting is proposed for the nonlinear chaotic system. Then, based on the T-S fuzzy model and the proposed linear control scheme, the H-infinity controller design problem for nonlinear chaotic systems is characterized in terms of minimizing the attenuation level subject to some linear matrix inequalities (LMIs), which is also called eigenvalue problem (EVP), through the scanning of a positive parameter. Finally, the proposed control scheme is applied to a chaotic system, namely Chua's circuit, to illustrate the robust performance of the proposed linear controller and linear observer.