Abstract: For T-S fuzzy systems with time-domain hard constraints and external disturbances,an H_∞ control scheme on the framework of LMI(linear matrix inequality) optimization is proposed.First,sufficient conditions satisfying the given H_∞, performance indexes are given and the ellipsoid set including the initial state is appointed.Then,under the bound assumption of the disturbance energy,another ellipsoid containing all perturbed trajectories is determined.Finally,the double-ellipsoid method is used to translate time-domain hard constraints into LMI conditions.This multi-objective design finally becomes an optimization problem to solve the LMI constraints.Simulation results of TORA(translational oscillator with an eccentric rotational proof mass actuator) system show that the proposed sheme is effective.