Eigenvalue placement for generalized linear systems

This paper deals with some aspects of eigenvalue placement by state feedback for generalized linear systems described by E = Ax + Bu , where E is a singular map. It is shown that controllability of the infinite eigenvalues of the pencil ( sE − A ) is equivalent to the existence of a state feedback map which assigns those eigenvalues to pre-specified complex numbers. A procedure for the assignment of all eigenvalues to distinct complex numbers is also discussed.