This paper studies poly-quadratic stability of nonlinear systems represented by a Takagi-Sugeno (T-S) discrete fuzzy model. A system is poly-quadratically stable when its stability can be verified by a parameter dependent Lyapunov function. There are already some results in this area. This paper, however, presents less conservative results by adopting more slack-matrix-variables in the linear matrix inequalities (LMIs). The parallel distributed compensation (PDC) law is utilized in both the anal