Minimum norm regularization of descriptor systems by mixed output feedback

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.