H₂ guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

This paper presents a design method of H₂ guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H₂ GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H₂ performance index. Furthermore, an optimal H₂ GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.