Asymptotic behaviour of Toeplitz matrix in multi-input multi-output model predictive control

The singular value decomposition of (SVD) of the Toeplitz matrix in the quadratic performance index of Model Predictive Control (MPC) is studied. The underlying goal is to find connection between the frequency domain information and the finite time optimal control and use this connection as a basis for stability, robust performance analysis and tuning of the dynamic MPC criterion. In a recent work by the authors, it was shown that the singular value decomposition of the Toeplitz matrix provides gain and phase information of the associated system for sufficiently long prediction and control horizons. This work is extended to MIMO case and is shown that singular value decomposition of the Toeplitz matrix can be used for stability analysis of closed loop system.