The parametric solutions of eigenstructure assignment for controllable and uncontrollable singular systems

Abstract

The previous results about the parametric solutions of eigenstructure assignment for singular systems applied by pure proportional or proportional-plus-derivative state feedback can only apply to controllable systems. It is because the parametric solutions of the right generalized eigenvectors corresponding to the infinite and uncontrollable finite eigenvalues have still not been found. In this paper, the parametric solutions of the right generalized eigenvectors for finite controllable (or uncontrollable) eigenvalues and infinite controllable (or uncontrollable) eigenvalues, when the system is applied by pure proportional or proportional-plus-derivative state feedback, are given. Hence, the parametric solution of eigenstructure assignment can be used to design the state feedback of both the controllable and uncontrollable systems. The condition for detecting the regularity of the resulting system is also given. © 2000 Academic Press.