Model Predictive Control for Interval Type-2 Fuzzy Systems with Unknown Time-Varying Delay in States and Input Vector

The time-varying delay is a peculiar phenomenon that occurs in almost all systems. It can cause numerous problems and instability during system operation. In this paper, the time-varying delay is considered in both the states and input vectors, which is a significant distinction between the proposed method here and previous algorithms. Furthermore, the time-varying delay is unknown but bounded. To address this issue, the Razumikhin approach is applied to the proposed method, as it incorporates a Lyapunov function with the original non-augmented state space of the system models, in contrast to the Krasovskii formula. Moreover, the Razumikhin method performs better and avoids the inherent complexity of the Krasovskii method, particularly when dealing with large delays and disturbances. For achieving output stabilization, the model predictive control (MPC) is designed for the system. The considered system in this paper is an interval type-2 (IT2) fuzzy T-S model, which provides a more accurate estimation of the dynamic model of the system. The online optimization problems are solved using linear matrix inequalities (LMIs), which reduces the computational burden and online computational costs compared to offline and non-LMI approaches. Finally, an example is provided to illustrate the effectiveness of the proposed approach.