Improvements on local non-quadratic stability of Takagi-Sugeno models

The present paper proposes simple and effective ways to improve recent results on the estimation of the region of attraction of continuous-time Takagi-Sugeno (TS) models. These estimates are obtained via a novel non-quadratic local stability approach that overcomes infeasible global quadratic conditions. In order to ameliorate these solutions two techniques are proposed to successively obtain better estimations of the stability domain: if a nonlinear model is available, an algorithm alternating closer modeling areas and bigger estimates comes in handy; if not, an algorithm alternating closer polytopes and bigger estimates proves useful. Conditions are expressed as linear matrix inequalities (LMIs) and progressively better estimates of the region of attraction are obtained via linear programming techniques. Some examples are included to illustrate the improvements.