Stability fuzzy controller design for affine fuzzy systems using a descriptor system approach

The problems of stability analysis and control synthesis for affine fuzzy systems are investigated by using a descriptor system approach. In most of pioneer works for closed-loop affine fuzzy systems, the sufficient stability conditions are cast in terms of bilinear matrix inequalities (BMIs), which is a difficult issue for designers. In this paper, the affine fuzzy systems are formulated as descriptor representation at first. Then, based on fuzzy Lyapunov functions, the sufficient stability conditions of the closed-loop systems are derived in terms of linear matrix inequalities (LMIs), rather than BMIs. Hence, the relaxed stability conditions can be easily solved by convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed approach.