An ILMI approach to robust H2H2 static output feedback fuzzy control for uncertain discrete-time nonlinear systems

This paper studies the problem of robust H2H2 static output feedback (SOF) fuzzy control for discrete-time nonlinear systems with parametric uncertainties. The Takagi and Sugeno fuzzy model is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of robust H2H2 SOF fuzzy controllers is presented in terms of a set of matrix inequalities, which not only guarantees the stability of the closed-loop fuzzy system, but also provides an upper bound on the quadratic cost function. A suboptimal robust H2H2 SOF fuzzy control problem is addressed in the sense of minimizing the bound. An iterative linear matrix inequality (ILMI) algorithm is proposed to compute the feedback gain matrices of the suboptimal fuzzy controller. Finally, two numerical examples are also provided to demonstrate the effectiveness of the proposed method.