This paper proposes a discrete state predictive control by introducing a virtual system. To determine the state-space model and the time delay, the subspace identification method, called CCA(Canonical correlation analysis) method, is applied. The CCA method can judge orders of the system by checking how many singular values of a covariance matrix among input-output data are near 1. First, the time system is shown to be identified by a higher-dimensional system, and this model can be used to the

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... LQG control for the time delay system. After that, by confirming the number of singular values near 1 according to time-shift operations between input-output data, the time delay can be identified and used it for the discrete state predictive control. The proposed method is applied to the stable vibration cart type pendulum with time delay inserted in artificially.