Applications of generalized Sylvester matrix equations in the design of eigenstructure assignment

Applications of a class of generalized second-order Sylvester matrix equations in the design of eigenstructure assignment are investigated. By using some elementary matrix transformations, an analytical general solution of the generalized Sylvester matrix equation is obtained in an iterative form. Based on the proposed analytical general solution of the generalized Sylvester matrix equation, a parametric method of the state feedback eigenstructure assignment in a class of second-order linear systems is presented. This parametric method offers the parametric expressions for all the eigenvector matrices and the state feedback gain matrices. And this method includes all the design degrees. A numerical example shows the simplicity and effectiveness of the analytical general solution to the generalized Sylvester matrix equation and the parametric method of state feedback eigenstructure assignment.