Stability analysis of T-S fuzzy PD, PI, and PID control systems

We present a simple and systematic way of designing stabilization fuzzy PID (Proportional-Integral-Differential), PI (Proportional-Integral), and PD (Proportional-Differential) controllers for the T-S fuzzy model. The state space representations of the fuzzy PD, PI, and PID controllers are firstly presented. Then we equivalently transform the fuzzy PID (PI, or PD) control system into the fuzzy static output feedback control system. The fuzzy static output feedback controller design for the latter system can be efficiently solved via the existing numerical optimization methods with some conservatism. Consequently, the fuzzy PID (PI, or PD) controller can be derived due to the one-on-one correspondence between the fuzzy PID controller and the fuzzy static output feedback controller. We use a numerical simulation example to show the effectiveness of our proposed methods.