An original solution to overcome infeasible global quadratic conditions for stability of continuous-time nonlinear models via a Takagi-Sugeno (TS) representation has recently appeared. By changing the paradigm of global stability for something less restrictive a nice solution providing an estimation of the stability domain (local asymptotic conditions) is found, as it is usually the case for nonlinear models for which stability and/or stabilization cannot be reached globally. Strategies to get better estimations with lower computational cost are hereby presented to fully exploit the new approach; some hard nonlinear problems are thus systematically solved. Since the proposed conditions are expressed as linear matrix inequalities (LMIs) they can be efficiently solved by convex optimization techniques. Illustrative examples are provided to show the efficiency of the new technique which outperforms available stability analysis by escaping the quadratic framework.