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The recently-proposed method for iterative correlation-based controller tuning is considered in this paper for the tuning of multivariable Linear Time-Invariant (LTI) controllers. The parameters of the controller are updated directly using the data acquired in closed-loop operation. This approach allows one to tune some elements of the controller transfer function matrix to satisfy the desired closed-loop performance, while the other elements are tuned to mutually decouple the closed-loop outputs. The controller parameters are calculated by minimization of the cross-correlation function involving instrumental variables. A very simple choice of the instruments is proposed. The approach is applied to a simulation model of a gas turbine engine, and excellent results are obtained in terms of decoupling and performance.