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The linearized differential equations describing the dynamics of an electrical power system are developed in polynomial matrix form. This reduces the number of variables from the state variable form of the equations, keeping only those appearing at the interface between the generating units and the transmission system. Algorithms are described which allow the eigenvalues to be assigned to a system described in this form, and allow the eigenvectors to approximate a desired set of eigenvectors. An example from the problem of forming a reduced order model of a power system is given.