In this paper, the model predictive control is designed for an interval
type-2 Takagi-Sugeno (T-S) system with unknown time-varying delay in state and
input vectors. The time-varying delay is a weird phenomenon that is appeared in
almost all systems. It can make many problems and instability while the system
is working. In this paper, the time-varying delay is considered in both states
and input vectors and is the sensible difference between the proposed method
here and previous algorithms, besides, it is unknown but bounded. To solve the
problem, the Razumikhin approach is applied to the proposed method since it
includes a Lyapunov function with the original nonaugmented state space of
system models compared to Krasovskii formula. On the other hand, the Razumikhin
method act better and avoids the inherent complexity of the Krasovskii
specifically when large delays and disturbances are appeared. To stabilize
output results, the model predictive control (MPC) is designed for the system
and the considered system in this paper is interval type-2 (IT2) fuzzy T-S that
has better estimation of the dynamic model of the system. Here, online
optimization problems are solved by the linear matrix inequalities (LMIs) which
reduce the burdens of the computation and online computational costs compared
to the offline and non-LMI approach. At the end, an example is illustrated for
the proposed approach