In this note, linear time-invariant descriptor-variable systems are co
nsidered which are either nonregular or, if they are regular, they hav
e impulsive modes. It is shown that if a certain necessary and suffici
ent condition is satisfied, then both regularity can be established an
d impulsive modes can be eliminated by output feedback. We have also c
onsidered the problem of achieving structural properties of the regula
rized system.