An extensive analysis on the existing results for the stability of TakagiSugeno fuzzy control is given. For the Lyapunov functions, the common quadratic Lyapunov functions, piecewise quadratic Lyapunov functions, fuzzy Lyapunov functions, nonquadratic Lyapunov functions and homogenously polynomially parameterized Lyapunov functions are considered. For the control laws, the parallel distributed compensation laws, nonparallel distributed compensation laws and homogenously polynomially parameterized control laws are considered. Based on the analysis, by applying the Polya's theorem and the techniques for homogenous polynomials, the approaches for approximating the necessary and sufficient conditions for stability of TS fuzzy control are given.