Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation

In this paper, the Takagi-Sugeno (TS) fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. In our TS fuzzy representation, the modeling error is also captured by norm-bounded uncertainties. A set invariance condition for the fuzzy system is first established. The problem of estimating the domain of attraction of a TS fuzzy system is formulated and solved as an LMI optimization problem. By viewing the state feedback gain as an extra free parameter in the LMI optimization problem, we arrive at a method for designing state feedback gain that maximizes the domain of attraction. A fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction. An inverted pendulum is used to show the effectiveness of the proposed fuzzy controller.