Abstract
A generalization of polynomial interpolation to the matrix case is introduced and applied to problems in systems and control. It is shown that this generalization is most general and it includes all other such interpolation schemes that have appeared in the literature. The polynomial matrix interpolation theory is developed and then applied to solving matrix equations; solutions to the diophantine equation are also derived. The relation between a polynomial matrix and its characteristic values and vectors is established and it is used in pole assignment and other control problems. Rational matrix interpolation is discussed; it can be seen as a special case of polynomial matrix interpolation. It is then used to solve rational matrix equations including the model matching problem.
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