Controller design for affine fuzzy systems via characterization of dilated linear matrix inequalities

We study the design of a state feedback controller for a class of nonlinear systems described by continuous-time affine fuzzy models. By introducing extra slack variables, the Lyapunov matrix and the system matrix are decoupled such that the controller parametrization is independent of the Lyapunov matrix. A novel quadratic stability analysis condition for affine fuzzy systems is derived in the formulation of linear matrix inequalities (LMIs), which is equivalent to existing results. Using the analytical results and a diffeomorphic state transformation, a stabilizing condition under which the affine fuzzy system is quadratically stabilizable is derived and can be solved by means of an LMI technique in conjunction with a search for scaling parameters. In contrast to existing work, the stabilizability condition we derive leads to less conservative LMI characterizations. The result is also extended to H∞ state feedback synthesis. Finally, a numerical example illustrates the merits of the new results.