A new theory to describe the asymptotic optimal closed-loop pole positions and their related eigenvectors is presented. This is accomplished by utilizing the optimal return difference relation in a matrix/input vector description of the asymptotic eigenstructure. The paper contains an analysis for the finite closed-loop positions showing that for nonsquare systems, there can be finite closed loop-poles not associated with the system invariant zeros. Also presented is an elementary analysis for the asymptotically infinite closed-loop pole positions. Introduced here are the concepts of Butterworth patterns and some simple subspace characterisations of the input vector directions.

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