A way to escape from the quadratic framework

Abstract

The results offered in this paper constitute a way to overcome infeasible global quadratic conditions for stability of continuous-time Takagi-Sugeno (TS) models. It is shown that reducing global stability goals to something less restrictive will give a nice solution by providing an estimation of the stability domain (local asymptotic conditions), as it is usually the case for nonlinear models for which stability and/or stabilization cannot be reached globally. Conditions under the novel approach can be expressed as linear matrix inequalities (LMIs) which are efficiently solved by convex optimization techniques. Some examples are provided to illustrate how the proposed technique actually broadens stability analysis by leaving the quadratic framework.