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We consider the classic problem of pole placement by state feedback. We offeran eigenstructure assignment algorithm to obtain a novel parametric form forthe pole-placing feedback matrix that can deliver any set of desiredclosed-loop eigenvalues, with any desired multiplicities. This parametricformula is then exploited to introduce an unconstrained nonlinear optimisationalgorithm to obtain a feedback matrix that delivers the desired pole placementwith optimal robustness and minimum gain. Lastly we compare the performance ofour method against several others from the recent literature.

A unified method for optimal arbitrary pole placement