Control Design for Parabolic PDE Systems via T–S Fuzzy Model

In this article, we investigate the parabolic partial differential equations (PDEs) systems with Neumann boundary conditions via the Takagi-Sugeno (T-S) fuzzy model. On the basis of the obtained T-S fuzzy PDE model, a novel fuzzy state controller which is associated with the boundary state of position and the mean value coefficient matrix derived through the mean value theorem of integral is designed to analyze the asymptotic stability of the parabolic PDE system. Without sampling the nonlinear parameter of the system, new stability conditions are deduced in the form of linear matrix inequalities (LMIs). Moreover, compared with the novel fuzzy state controller, more conservative conditions based on another fuzzy state controller are also provided. Finally, we explore the state-feedback controller into the Fisher equation as an application. Simulation results show that the proposed method is effective.