H_∞ fuzzy controller synthesis for large-scale systems with non-linear interconnections and disturbance

This study studies the H_∞ fuzzy controller design problem for a non-linear large-scale system with non-linear interconnections and disturbance. In the large-scale system, each subsystem, excluding non-linear interconnections and disturbance, is transformed into a Takagi-Sugeno fuzzy system and the nonlinear interconnections of each subsystem must satisfy a norm inequality. The number of rules for the large-scale system as a whole can be reduced through the use of the norm inequality because the interconnection terms do not need to be transformed into fuzzy rule sets and thus the controller synthesis will be much easier. On the other hand, the H_∞ performance can be improved by adjusting the weighting value of the norm inequality. The main theorems of this paper are obtained through the use of S-procedure and linear matrix inequality method. Lastly, the authors provide three examples to show the effectiveness of the proposed method.