Fuzzy control design for switched nonlinear systems

Recently, many researchers have devoted themselves to the study of methods of designing controllers for switched nonlinear systems with the use of the switched Takagi-Sugeno (T-S) fuzzy model. The main feature of switched T-S fuzzy models is that they characterize the local dynamics of each fuzzy rule by a linear model. The appeal of the switched T-S fuzzy model in control design is that the stability and performance characteristics of a system can be verified by using a Lyapunov function approach. Nevertheless, it should be noted that in a switched T-S fuzzy model, the consequence could be any functions. In this study, we attempt to study the control design problem of switched T-S fuzzy models, which have nonlinear consequence functions. The paper presents a novel switching fuzzy control design approach based on control Lyapunov function. The proposed approach can design stable controllers for a switched T-S fuzzy model of which the consequents are affine nonlinear state dynamic equations. The proposed switching fuzzy controller guarantees the stability of the closed loop switched systems. The Sontagpsilas formula developed for affine nonlinear control systems is employed to construct a switching T-S fuzzy controller. Based on a control Lyapunov function approach, we derive a sufficient condition to ensure the stability of the closed loop switched fuzzy systems. Two examples are given to show the advantage of the presented method.