H₂ guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities

This paper deals with H₂ guaranteed cost (GC) fuzzy control problem for uncertain continuous-time nonlinear systems. The state feedback case and observer-based output feedback case are considered. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with parametric uncertainties. Sufficient conditions for the existence of H ₂ GC fuzzy controllers are given in terms of linear matrix inequalities (LMIs). The suboptimal H₂ GC fuzzy controllers are given by means of the LMI optimization procedures, which cannot only guarantee that the closed-loop overall fuzzy systems are globally asymptotically stable, but also provide an optimized upper bound on the quadratic performance cost. Finally, an example is presented to illustrate the effectiveness of the proposed fuzzy controllers.