Interval type-2 regional switching T-S fuzzy control for time-delay systems via membership function dependent approach

Abstract

Abstract This paper investigates the stabilization problem of the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy-model-based control systems with time delay. We extend the type-1 switching T–S fuzzy model to deal with the IT2 T–S fuzzy model, and the new constructed model is defined as the IT2 regional switching T–S fuzzy model in this paper. Furthermore, a new type state feedback controller, namely IT2 regional switching fuzzy controller which switches according to system states, is designed to perform the control process. Then, based on the piecewise membership functions, the membership function dependent approach is adopted specifically for time-delay systems, and hence several stability criteria are derived by utilizing the relaxed Lyapunov–Krasovskii functional. Since the membership function dependent approach considers more information of lower and upper membership functions, the conservatism of the stability conditions is reduced. Finally, two numerical examples are provided to demonstrate that the theoretical results are effective and the membership function dependent approach plays an important role in relaxing the stability criteria.