Introducing shape-dependent relaxed conditions in fuzzy control of nonlinear systems in Takagi-Sugeno form

Most of the fuzzy literature presents stability and performance results in fuzzy control of Takagi-Sugeno models via LMI conditions; such conditions are independent of the particular shape of the LMIs. Shape-dependent conditions may be used to relax the results: some of them are only conditions on the memberships themselves; others include relations between state variables and memberships. The latter approach, then, enters into the realm of actual nonlinear control, departing from the conventional analysis which proves stability of nonlinear systems via proving stability of some linear time-variant convex-hull models (the Takagi-sugeno systems). The conditions may be made polynomial with the sum-of-squares approach. With the ideas in this paper, the gap between fuzzy and nonlinear control gets smaller.