This paper addresses the problems of local stability analysis, local stabilization, and computation of invariant subsets of the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems. Improvements on the existing stability and stabilization conditions are achieved through the reduction of conservatism. To release the conservatism further, the so-called multidimensional fuzzy summation approach is adopted. The design and analysis conditions are expressed as one-parameter minimization problems which can be solved via a sequence of linear matrix inequality optimizations or treated as eigenvalue problems. Examples are given to show the validity of the proposed method.