A parametric solution of second-order vibration matrix equations and its control applications

Solution of a class of second-order vibration matrix equations is investigated. In the case of the eigenvalues with the Jordan diagonal canonical form, a parametric method is proposed, which offers the parametric expressions of the unknown matrices in the matrix equation. And by using the parametric solution to design the eigenstrucure assignment via the state feedback, parametric expressions of the state feedback gain matrices are proposed. Finally, a numerical example shows the simplicity and effectiveness of the proposed parametric method.