Robust H∞ control for Van de Vusse reactor via T-S fuzzy bilinear scheme

This paper proposes a fuzzy bilinear scheme including a fuzzy modeling method and a fuzzy controller for a class of uncertain nonlinear systems with an additive disturbance input. Firstly, this procedure of modeling describes how to transform a nonlinear system into a fuzzy bilinear system (FBS). For controller design problem, the parallel distributed compensation (PDC) method is adopted to design a fuzzy controller which ensures the robust asymptotic stability of the uncertain T-S FBS with an additive disturbance input and guarantees an H∞ norm bound constraint on disturbance attenuation. Besides, some sufficient conditions are derived to guarantee the robust stabilization of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, the Van de Vusse reactor (Chen, Lin, Lin, & Tong, 2008; Chong & Zak, 1996; Kashiwagi & Rong, 2002; Li, Tsai, Lee, Hsiao, & Chao, 2008; Perez, Ogunnaike, & Devasia, 2000) with additive disturbance input is utilized to demonstrate the validity and feasibility of the proposed control scheme.