Robust H∞ tracking controller design for discrete-time affine fuzzy system using fuzzy Lyapunov method

In this paper, the model reference tracking control problem is presented for the discrete-time affine fuzzy systems with external disturbances. The control scheme is based on H∞ performance to eliminate the effect of disturbances below a prescribed level. Based on fuzzy Lyapunov functions, the sufficient conditions are derived in the terms of bilinear matrix inequalities (BMIs) to ensure the close-loop system is uniformly ultimately bounded (UUB). A solving algorithm is proposed to convert BMIs to linear matrix inequalities (LMIs), which can be solved by LMI toolbox easily. Finally, the fuzzy tracking controller design method is used for a boiler-turbine generator unit (BTGU). The simulation shows the proposed stability approach is valid.