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Parametrization of proper, reduced structure MIMO tracking prefilters with optimality considerations

This paper presents a multivariable extension to work of Jayasuriya et al. (1993). It also presents a method for obtaining optimality in some sense. We consider the problem of continuous tracking of a vector of reference signals, where each signal is assumed to be a linear combination of polynomials, exponentials and sinusoids of known frequencies. The issue is to construct a system such that the performance is optimized, subject to the constraint of zero preview information. The concept of orthogonality, is used to construct a prefilter with zero preview information through the solution of a matrix Diophantine equation. This method allows the zero structure of the final sensitivity function to be chosen with great freedom. In addition, we exploit the non-uniqueness of the solution to the matrix Diophantine equation to obtain a prefilter that is optimal in some sense.