Design of a stable Takagi-Sugeno Fuzzy Control system via LMIs with disturbance rejection

In this paper, we have presented the control of an inverted pendulum system controlled by a dc motor via a gear train using the T-S fuzzy approach. Stability conditions of this system with disturbance rejection can be formulized in terms of linear matrix inequalities (LMIs), which can be solved using the LMI Toolbox in MATLAB. To simplify the procedure of T-S fuzzy modeling and control, a software tool designed by the authors was proposed which is called the “Modeling Takagi-Sugeno Fuzzy Control Toolbox”. This toolbox works in Matlab/Simulink environment.