  In this paper, we propose a new systematic approach based on nonquadratic
Lyapunov function and technique of introducing slack matrices, for a class of
affine nonlinear systems with disturbance. To achieve the goal, first, the
affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear
model. Subsequently, the robust H_inf controller is designed based on parallel
distributed compensation (PDC) scheme. Then, the stability conditions are
derived in terms of linear matrix inequalities (LMIs) by utilizing Lyapunov
function. Moreover, some slack matrices are proposed to reduce the
conservativeness of the LMI stability conditions. Finally, for illustrating the
merits and verifying the effectiveness of the proposed approach, the
application of an isothermal continuous stirred tank reactor (CSTR) for Van de
Vusse reactor is discussed in details.
