Beschreibung:
We study the regularization problem for linear, constant coefficient descriptorsystems$E x^. =AX + Bu, y_1 = Cx, y_2=\Gamma x^.$by proportional and derivativemixed output feedback. Necessary and sufficient conditions are given, which guaranteethat there exist output feedbacks such that the closed-loop system is regular, hasindex at most one and$E +BG\Gamma$hasa desired rank, i.e. there is a desired number of differential and algebraic equations.To resolve the freedom in the choice of the feedback matrices we then discuss howto obtain the desired regularizing feedback of minimum norm and show that this approachleads to useful results in the sense of robustness only if the rank ofEisdecreased. Numerical procedures are derived to construct the desired feedbacks gains.These numericalprocedures are based on orthogonal matrix transformations whichcan be implemented in a numerically stable way.