Invariant zeros and zero-directions of multivariable linear systems with slow and fast modes

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Abstract
It is shown that the asymptotic values of the invariant zeros and associated zero-directions of multivariable systems with ‘slow’ and ‘ fast ’ modes can be readily computed by considering separately the system matrices associated with the ‘ slow ’ and ‘ fast ’ sub-systems of such systems. The general results are illustrated by determining both the ‘ slow ’ and ‘ fast ’ invariant zeros and associated zero-directions of a third-order system with ‘ slow ’ and ‘ fast ’ modes.