Synthesis of distributed sampled-data fuzzy controller for a class of hyperbolic PDE systems

This paper investigates the problem of designing sampled-data fuzzy controller for a class of nonlinear hyperbolic partial differential equation (PDE) systems. By using the sector nonlinearity approach, the exact Takagi-Sugeno (TS) hyperbolic PDE fuzzy model will be obtained. Then, based on the spatially distributed parallel distributed compensation (SDPDC), the closed-loop system will be achieved via an input delay approach. Then, based on the proposed spatially distributed Lyapunov Krasovskii functional (LKF) and also introducing some new null terms, the sufficient stability conditions will be calculated in terms of linear matrix inequalities (LMIs). Finally, the proposed approach is applied to non-isothermal Plug flow reactor (PFR) to illustrate the effectiveness of the proposed approach.