We investigate the changes under small perturbations of the canonical structure
information for a system pencil (A B C D) - s (E 0 0 0), E is nonsingular, associated with a (generalized) linear time-invariant state-space system. The equivalence
class of the pencil is taken with respect to feedback-injection equivalence
transformation. The results allow to track possible changes under small perturbations
of important linear system characteristics.