Adaptive fuzzy control of nonlinear systems based on multiple inputs T-S fuzzy bilinear model

This paper presents the design scheme of stable adaptive fuzzy control for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is employed to represent the systems. First, the parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error caused by fuzzy modeling and the sufficient conditions with respect to decay rate α are derived by linear matrix inequalities (LMI). Then, the error caused by fuzzy modeling is considered and the method of adaptive control is used to reduce the effect of the modeling error, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.