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This paper introduces a solution to the partial eigenvalues assignment problem of high order linear systems with time delayed system in both single-input and multi-input cases using orthogonality relations between eigenvectors of the matrix polynomial. The solution requires the knowledge of only a few eigenvalues and with corresponding left eigenvectors of matrix polynomial. The numerical examples are done to illustrate the proposed method. Theorem 1: (Sarkissian, 2001) Orthogonality of thedoi:10.3844/ajassp.2016.1006.1013 fatcat:6ndwwlu43jgsjkbxpnduznbs5y