Problem of regularization of a singular system by derivative and proportional
output feedback is studied. Necessary and sufficient conditions are obtained under
which a singular system can be regularized into a closed-loop system that is regular
and of index at most one. The reduced form is given that can easily explore the
system properties as well as the feedback to be determined. The main results of
the present paper are based on orthogonal transformations. Therefore, they can
be implemented by numerically stable ways.