Automatica, Vol.42, No.7, 1183-1188, 2006
H-2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty
This paper presents a design method of H-2 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 H-2 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 H-2 performance index. Furthermore, an optimal H-2 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. (c) 2006 Elsevier Ltd. All rights reserved.
Keywords:discrete-time nonlinear systems;fuzzy control;linear matrix inequality (LMI);Takagi and Sugeno fuzzy model