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In this paper, the model predictive control is designed for an intervaltype-2 Takagi-Sugeno (T-S) system with unknown time-varying delay in state andinput vectors. The time-varying delay is a weird phenomenon that is appeared inalmost all systems. It can make many problems and instability while the systemis working. In this paper, the time-varying delay is considered in both statesand input vectors and is the sensible difference between the proposed methodhere and previous algorithms, besides, it is unknown but bounded. To solve theproblem, the Razumikhin approach is applied to the proposed method since itincludes a Lyapunov function with the original nonaugmented state space ofsystem models compared to Krasovskii formula. On the other hand, the Razumikhinmethod act better and avoids the inherent complexity of the Krasovskiispecifically when large delays and disturbances are appeared. To stabilizeoutput results, the model predictive control (MPC) is designed for the systemand the considered system in this paper is interval type-2 (IT2) fuzzy T-S thathas better estimation of the dynamic model of the system. Here, onlineoptimization problems are solved by the linear matrix inequalities (LMIs) whichreduce the burdens of the computation and online computational costs comparedto the offline and non-LMI approach. At the end, an example is illustrated forthe proposed approach.

Designing the Model Predictive Control for Interval Type-2 Fuzzy T-S Systems Involving Unknown Time-Varying Delay in Both States and Input Vector