We study the regularization problem for linear, constant coefficient descri
ptor systems E(x)over dot = Ax + Bu, y(1) = Cx, y(2) = Gamma(x)over dot by
proportional and derivative mixed output feedback. Necessary and sufficient
conditions are given, which guarantee that there exist output feedbacks su
ch that the closed-loop system is regular, has index at most one and E + BG
Gamma has a desired rank, i.e., there is a desired number of differential
and algebraic equations. To resolve the freedom in the choice of the feedba
ck matrices we then discuss how to obtain the desired regularizing feedback
of minimum norm and show that this approach leads to useful results in the
sense of robustness only if the rank of E is decreased. Numerical procedur
es are derived to construct the desired feedback gains. These numerical pro
cedures are based on orthogonal matrix transformations which can be impleme
nted in a numerically stable way. (C) 1999 Elsevier Science Inc. All rights
reserved.