SUFFICIENT AND ASYMPTOTIC NECESSARY CONDITIONS FOR THE STABILIZATION OF TAKAGI-SUGENO MODEL

Controller design for Takagi-Sugeno models are mostly expressed as LMI conditions. Deriving these conditions consist in the use of the direct Lyapunov method and usually with the quadratic candidate Lyapunov function. The conditions obtained are in the form a matrix inequality involving a double convex-sum. In order to deal with this double convex-sum, there exist some results called relaxations. These latter ones give only sufficient conditions to ensure the quadratic stabilization. The paper gives a methodology to reduce the conservatism of these relaxations and make them asymptotically necessary and sufficient.