Design of robust H_inf fuzzy output feedback controller for affine nonlinear systems:Fuzzy Lyapunov function approach
This work addresses control design for nonlinear systems like chemical reactors, but it appears incremental as it builds on existing fuzzy and LMI methods.
The authors tackled the problem of designing robust H_inf fuzzy output feedback controllers for affine nonlinear systems with disturbances, achieving stability conditions expressed as linear matrix inequalities (LMIs) with reduced conservativeness through slack matrices.
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.