An integrated fuzzy control system design for nonlinear systems-fuzzy modeling and robust controller design via LMIs

This paper presents an integrated LMI approach to fuzzy modeling and controller design for nonlinear systems with unknown parameters. The main feature is to achieve iteratively and effectively fuzzy modeling and controller design. Three LMI conditions to identify the parameters of a Takagi-Sugeno fuzzy model (T-S fuzzy model) are derived. More importantly, we design a robust controller that compensates the identification error occurred in the fuzzy modeling part. The main idea is to transform the error into uncertainty in the T-S fuzzy model and to design a robust fuzzy controller by robust stability LMI conditions newly derived in this paper. A design example shows the utility of the integrated LMI approach to fuzzy modeling and controller design.