Delay-dependent stabilization of discrete-time interval type-2 T-S fuzzy systems with time-varying delay

This study focuses on the stabilization problem of discrete-time interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. A new IT2 fuzzy state feedback controller that does not share the same membership functions and number of rules with the IT2 T-S fuzzy model is designed to close the feedback loop. A novel fuzzy Lyapunov-Krasovskii function (FLKF) is introduced based on the delay partitioning technique to derive the existence conditions of the IT2 fuzzy state feedback controller. The proposed FLKF does not require all the involved symmetric matrices to be positive definite. Several advanced inequalities and the boundary information on membership functions are used to achieve delay-dependent stabilization conditions in terms of linear matrix inequalities. Two numerical examples are provided to show the effectiveness of the proposed approach.