Theory and computations of some inverse eigenvalue problems for the quadratic pencil (Q2784655)

The main interest of the authors is focused on certain types of inverse eigenvalue problems associated with a quadratic matrix pencil arising in feedback control of a matrix second-order system.NEWLINENEWLINENEWLINEThe paper is organized as follows, in section 2, Orthogonality relations of the eigenvectors of quadratic matrix pencils, the authors derive three orthogonality relations between the eigenvectors of a symmetric definite quadratic pencil. Section 3, Modal criterion of controllability, treats the Hantus criterion of controllability to the second-order system. Section 4, Solution to problem 1.1, is divided in two subsections and presents a direct partial modal approach for solving the mentioned problem. Section 5, Solution to problem 1.2, gives the solution to the partial eigenstructure assignment for a quadratic pencil and is followed by Illustrative numerical examples. Finally, section 7 contains conclusions and remarks on future research.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00034].