This paper addresses the H∞ finite-time control problem subject to a state constraint of the partial differential equation (PDE) for a class of coupled systems described by nonlinear ordinary differential equations (ODEs) and a linear parabolic PDE.Initially, based on the data collected from the PDE system, the Karhunen-Loève decomposition (KLD) is utilized to compute the empirical eigenfunctions (EEFs).Along with those EEFs, the singular perturbation technique is applied to the PDE system to derive a finite dimensional ODE model which accurately describes the dynamics of the dominant (slow) modes of the PDE system.By combining the original ODE system with the slow model of the PDE system, a nonlinear coupled ODE system is obtained, which is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model.Meanwhile, the PDE state constraint is converted into a state constraint exerted on the coupled ODE system.Then, based on the fuzzy model, an H∞ fuzzy control design is developed in terms of linear matrix inequalities (LMIs), to stabilize the original ODE system in a finite time with a terminal time as small as possible, and achieve an optimized H∞ performance of disturbance attenuation for the coupled ODE system, while the PDE state constraint is respected.Finally, the proposed design method is applied to the control of a hypersonic rocket car to illustrate its effectiveness.