Polynomial Controller Synthesis for Uncertain Large-Scale Polynomial T–S Fuzzy Systems

This paper proposes a novel method to synthesize a controller for stabilizing the nonlinear large-scale system which is represented by a large-scale polynomial Takagi–Sugeno (T–S) fuzzy system. The large-scale system consists of a set of the uncertain polynomial T–S fuzzy system with interconnection terms. Modeling the large-scale nonlinear system under the framework of the polynomial form will decrease both the modeling errors and the number of fuzzy rules with respect to the conventional large-scale T–S fuzzy system. In addition, because of the existence of uncertainties, the synthesizing controller for the large-scale polynomial fuzzy system becomes much more challenging and has not been investigated in the previous studies. In this paper, a controller is synthesized to simultaneously eliminate the impact of the uncertainties and stabilize the system. With the aid of Lyapunov theory, sum-of-square technique, and S-procedure, the conditions for controller synthesis are derived in the main theorems. Finally, two examples are illustrated to show the effectiveness and merit of the proposed method.