Closed forms for the Levinson coefficients of polynomial compensators and inverse systems

The least-squares transformation of a discrete-time multivariable linear system into a desired system by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution of a normal linear matrix equation whose coefficients are shown to be the weighting patterns of certain linear systems. These can then be used in the recursive solution of the normal equation.<
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