Abstract: Introducing a special matrix measure and based on the elementary properties of M-matrices, the stability of T-S fuzzy systems is analyzed, and shows that the stability of a judgement matrix constructed by the coefficient matrices of related subsystems implies the global stability of the T-S fuzzy systems. This algebraic stability criterion is different from the existing results which are usually obtained within the framework of Lyapunov stability. Then, according to PDC arithmetic, a controller design method with fuzzy state feedback is given using the algebraic criterion as well as a necessary condition given to the stability of the closed-loop T-S fuzzy system's judgment matrix. An example is presented to demonstrate the method.