Abstract: The admissible conditions and H∞ control problem of T-S fuzzy descriptor systems are introduced. The original systems can be generalized to augmented systems, then some admissible conditions for fuzzy descriptor systems are obtained based on a new fuzzy Lyapunov function and new fuzzy controller. For the admissible conditions of open-loop systems, the subsystems are not required to be admissible, nor the multiplied term of input control matrix by control gain matrix has to be considered in the admissible conditions of closed-loop systems. By virtue of the property of membership function, the H∞ control conditions are improved. Furthermore, some strict linear matrix inequalities (LMIs) are obtained. At last, some examples are given to illustrate that the obtained sufficient conditions are less conservative than the results given by previous literature.