Stabilization of interval type-2 T-S fuzzy control systems with time varying delay

This paper studies the delay-dependent stabilization problem for interval type-2 fuzzy controller design of continuous-time interval type-2 Takagi-Sugeno (T-S) systems with time-varying delay. A delayed interval type-2 T-S fuzzy model is used to represent the state-space equation for a class of continuous nonlinear systems with time delay subject to parameter uncertainties. Then, a stable interval type-2 T-S fuzzy controller is designed, which guarantees asymptotic stability for the closed-loop interval type-2 fuzzy system with time-varying delay. A delay dependent sufficient condition for the existence of such a stabilizing controller is established in terms of the linear matrix inequality (LMI) by employing a novel common Lyapunov-Krasovskii (L-K) functional approach and a newly proposed tighter bounding technique based on the reciprocally convex combination idea. It provides a first attempt to tackle with the stabilization problem of type-2 fuzzy systems with time-varying delay.