Some refinements for non quadratic stabilization of continuous TS models

Quadratic stability / stabilization / estimation for Takagi-Sugeno models have now reached maturity. Lots of results concerning performances (H₂, H_∞, D-stability) for TS models with uncertainties, noise, time-delays ... exist in the literature. Nevertheless, it is illusive thinking to solve every nonlinear problem of stability using a simple quadratic Lyapunov function. Moreover, most of the nonlinear systems only have properties of local stability. This work follows the idea of using non quadratic Lyapunov functions for continuous Takagi-Sugeno models restricting the global asymptotic stability to a local one. Therefore, it tries to estimate the best stabilization domain possible. A rather "simple" LMI constraints problem is derived to answer to this question.