Tracking control design of interval type-2 polynomial-fuzzy-model-based systems with time-varying delay

In this paper, the tracking control design for the interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) control system subject to time-varying delay situation is investigated. The tracking control system is formed of the IT2 polynomial fuzzy model representing a nonlinear system with time-varying delay, the stable reference model and the IT2 polynomial fuzzy controller. The control objective is to design a proper IT2 polynomial fuzzy controller which is capable of driving the states of the polynomial fuzzy model to track those in the reference model and the tracking performance is evaluated and improved by the H∞ performance index. Also, to handle the uncertainty in the membership functions, the property of IT2 fuzzy sets is utilized to enhance the fuzzy controller's robustness against uncertainty. In addition, considering the effect of time-varying delay, the Lyapunov-Krasovskii functional based approach is adopted to facilitate the delay-dependent stability analysis. Stability conditions depending on the time-varying delay characteristic with the consideration of H∞ performance are obtained in terms of sum-of-squares (SOS). Furthermore, the information of the IT2 membership functions is employed in the stability analysis to relax the stability conditions, both membership-function-independent (MFI) and membership-function-dependent (MFD) approaches are presented to develop the stability conditions. Simulation examples are presented to verify the effectiveness of the proposed tracking control approach.