Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case

This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition Is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In synthesis, the stabilizability condition turns out to be in the formulation of nonconvex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.