Partial eigenvalue assignment problem of linear control systems using orthogonality relations

Abstract

The partial eigenvalue assignment is the problem of reassigning a part of the open-loop spectrum of a linear system by a feedback control, leaving the rest of the spectrum invariant. In the paper, we propose a novel solution to the partial eigenvalue assignment problem of linear control system using orthogonality relations between eigenvectors of the state matrix . Our solution can be implemented with only a partial knowledge of the spectrum and the corresponding eigenvectors of the linear system. We show that, the number of eigenvalues and eigenvectors that need to remain unchanged will not be affected by the feedback. We prove this, the feedback vector must be of real form. A numerical example is given to illustrate the proposed method.

Keywords

• linear control systems
• orthogonality relations
• eigenvectors
• matrix