Sampled-Data Fuzzy Observer Design for Semilinear Parabolic PDEs

In this paper, the sampled-data fuzzy observer design problem is addressed for semilinear parabolic partial differential equations (PDEs). Initially, the semilinear PDE system is accurately represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T-S fuzzy model, a time-dependent Lyapunov functional is used to design a sampled-data fuzzy observer such that the estimation error PDE system is exponentially stable and satisfies an H
_∞
performance to attenuate the effect of the design disturbance. The stabilization condition is presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the FitzHugh-Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.