Subpredictor-Based Fuzzy Control Design for a Reaction–Diffusion Equation

This article addresses the stabilization of nonlinear reaction–diffusion equation with an unknown but bounded delay. Based on Takagi–Sugeno (T–S) fuzzy rules, a T–S partial differential (PDE) model is constructed to describe distributed parameter system. More importantly, we contribute large delay compensation and future state prediction by introducing chain subpredictors for PDE model, convergence observation errors guaranteed as well. Different from conventional approaches, proposed observer can compensate larger To stabilize system, first time, new subpredictor-based control law suggested using observer, which composed elementary observers connected in series. The implementation subpredictor feedback simpler than classical methods that only one employed. Via Lyapunov–Krasovskii approach, sufficient exponential stability conditions are established framework linear matrix inequalities. A numerical example provided illustrate effectiveness theoretical results.