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Eigenstructure Assignment in Second-order Linear Systems: A Parametric Design Method

Eigenstructure assignment via the proportional-plus-derivative feedback in second-order linear systems is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom, which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.