Analysis and design of an affine fuzzy system via bilinear matrix inequality

In this paper, a novel analysis and design method for affine fuzzy systems is proposed. Both continuous-time and discrete-time cases are considered. The quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities (BMIs). Two diffeomorphic state transformations (one is linear and the other is nonlinear) are introduced to convert the plant into more tractable affine form. The conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality (LMI) technique. The bias terms of the fuzzy controller are solved simultaneously together with the gains. Finally, the applicability of the suggested method is demonstrated via an example and computer simulation.