Assignment of Eigenstructure by Use of Polynomial Matrices

This paper looks at the problem of eigenstructure assignment using output feedback. It solves the eigenvector and eigenvalue assignment for any system with output feedback by characterizing the solutions as polynomial matrices. It presents the concept of an annihilating polynomial matrix product to enable the space containing the eigenvectors to be described by a matrix polynomial. The range of eigenvectors is expressed as a polynomial vector for the achievable closed-loop spectrum, which is also expressed as a diagonal polynomial matrix. Two examples are given to illustrate the technique both for single-input and multi-variable systems.