Affine parallel distributed compensator design for affine fuzzy systems via fuzzy Lyapunov function

• More relaxed stability analysis conditions based on nonquadratic fuzzy Lyapunov function and affine parallel distributed compensation.
• H∞H∞ controller to reject the disturbances.
• Disturbance rejection of nonlinear synchronous generator system.

This paper develops a novel stability analysis and robust controller design method for affine fuzzy systems. The emphasis of the paper is to present more relaxed stability conditions based on nonquadratic fuzzy Lyapunov function and affine parallel distributed compensation. At first, diffeomorphic transformations are used to treat more general class of nonlinear systems in a unified manner. Then, by introducing slack matrices, the Lyapunov matrices are decoupled from the feedback gain matrices and controller affine terms which lead to eliminate the structural constraints of Lyapunov matrices and consequently reduces the conservativeness of the proposed approach. Because of the bias terms, the stabilization conditions are obtained in terms of bilinear matrix inequalities. A nonsingular state transformation together with using the S-procedure and also slack variables lead to derive the stabilization conditions in the formulation of linear matrix inequalities which can be solved by convex optimization techniques. Moreover, H∞H∞ controller is used to reject the disturbances. Finally, the merit and applicability of the proposed approach are demonstrated via comparative numerical and industrial case studies.