Improving disturbance rejection and tracking performance of interval type-2 T-S fuzzy systems with time-varying delay

In this paper, the issue of disturbances rejection for a class of interval type-2 T-S fuzzy systems (IT-2 TSFSs) with time-varying delay is studied. First, an augmented dynamic IT-2 TSFS composed of an internal model, observer, and improved equivalent input disturbance (IEID) is constructed. The IEID estimator is inserted into the fuzzy controller to compensate for unknown external disturbances. Meanwhile, a controller structure including state feedback, internal model feedforward, error feedback, and IEID is designed to improve the disturbance rejection performance of the IT-2 TSFSs. Then, the controller design problem is transformed into a stability problem of the augmented dynamic system. In addition, a Lyapunov-Krasovskii functional (LKF) is constructed which relies on the information of integral variables and membership functions (MFs). Using the time derivative information of the MFS, the controller with switching rules is designed. To reduce the conservatism of the system design conditions and improve the degree of freedom, the slack matrix and upper and lower MFs information are introduced in the stability analysis of the control system. Finally, the availability and advantages of our proposed method are validated through a numerical simulation.