Sampled-data fuzzy $$H_\infty$$ estimators for control of nonlinear parabolic partial differential equations

This study handles the robust sampled-data [Formula: see text] fuzzy control analysis for a category of nonlinear partial differential systems (NPDSs) holding disturbances. As for now, the Takagi-Sugeno (T-S) fuzzy model serves superior by describing a broad category of nonlinear systems, and therefore, originally, a T-S fuzzy model is employed to illustrate the nonlinear parabolic partial differential systems. Here, the primary focus of this research is on designing a resilient sampled-data [Formula: see text] fuzzy estimator-based controller which is competent in stabilizing the T-S fuzzy closed-loop partial differential systems (PDSs) and to tolerate the disruption under a specified level. By the virtue of Lyapunov stability theory, Green's formula and several inequality techniques, the robust stabilization design problem based on a sampled-data fuzzy [Formula: see text] estimator is effectively addressed using a set of linear matrix inequalities (LMIs). Moreover, the impacts of the diffusion phenomenon and the designed controller are clearly reflected in the derived criteria. Further, the acquired criteria can be checked for their practicability by the virtue of MATLAB LMI control toolbox. Finally, simulation results are presented to demonstrate the effectiveness of the proposed criteria.