Observer-Based Switching Control for T-S Fuzzy Systems with Mixed Time Delays

This paper considers the control problem of T-S fuzzy systems with mixed time delays. Based on the time derivative data of the membership function of T-S fuzzy systems, fuzzy Lyapunov functions are designed by two methods, and observer-based switching controllers are obtained. One is to design fuzzy Lyapunov functions by loosening the requirement of positive quality of symmetric matrices. The other approach takes the controller's form into account. First, the form of the system model is adjusted by comparing each state value involved in the system with the state value of the controller. Then, the fuzzy Lyapunov function is designed using the difference value of the comparison. Both of the above observer-based switching controllers can stabilize the system. Examples are provided to demonstrate the effectiveness of the switching controllers proposed in this paper.