Robust design of fuzzy controllers based on small gain conditions

In this paper, we study the robust stability problem for a feedback system with a fuzzy controller. The problem is treated using the Small-Gain and Conicity Criteria for nonlinear stability. Robustness is addressed in terms of multiplicative perturbations and stability margins. Compensator design is based on an initial set of rules (the previous design), reflecting an approximate formulation of the desired performance. The previous design is refined and modified to achieve a prescribed robustness margin. We impose in the design procedure that the required changes have to be as small as possible. In this way, the final solution is the better compromise between performance and robust stability. The redesign is based on inequalities on the fuzzy parameters (ouput centroids) that are derived from Small-Gain stability conditions. The proposed method has been successfully tested on the simulated model of an inverted pendulum.