Abstract
The robust state-feedback and output-feedback control designs for the N-dimensional linear and nonlinear parabolic partial differential systems (PDSs) with different boundary conditions (Dirichlet or Neumann boundary conditions) are realized with a completely new robust stabilization design methods in this study. With the help of the knowledge-based fuzzy system technique, the robust fuzzy full-controller and the robust fuzzy estimator-based controller are developed for the robust state-feedback and output-feedback control designs, respectively. In addition, the robust fuzzy area-controller and the robust fuzzy point-controller are proposed for the robust state-feedback control design to reduce the design cost. For the state-feedback case via the robust fuzzy full-controller, area-controller, and point-controller, their control efficiency and design cost are further discussed. In order to overcome the difficulty in resolving the control design problems for the PDSs, we provide a new approach to engineers with the traditional algebraic matrix techniques and robust control analysis for the control designs. Therefore, the robust fuzzy full-controller, area-controller, point-controller, and estimator-based controller are developed with a simple and general method to efficiently deal with the effect of partial derivatives on the PDSs. Finally, some simulation examples are given to verify the utility and capacity of the proposed control designs for PDSs.