Robust H₂ fuzzy output feedback control for discrete-time nonlinear systems with parametric uncertainties

This paper deals with the robust H₂ fuzzy observer-based control problem for discrete-time uncertain nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with parametric uncertainties. A fuzzy observer is used to estimate the state of the fuzzy system and a non-parallel distributed compensation (non-PDC) scheme is adopted for the control design. A fuzzy Lyapunov function (FLF) is constructed to derive a sufficient condition such that the closed-loop fuzzy system is globally asymptotically stable and an upper bound on the quadratic cost function is provided. A sufficient condition for the existence of a robust H₂ fuzzy observer-based controller is presented in terms of linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal fuzzy observer-based controller in the sense of minimizing the cost bound is proposed. Finally, an example is given to illustrate the effectiveness of the proposed design method.