Minimum norm regularization of descriptor systems by mixed output feedback (Q1124956)

The regularization problem for the linear time-invariant systems \(E\dot x= Ax+ Bu\), \(y_1= Cx\), \(y_2=\Gamma\dot x\) by mixed proportional and derivative output feedback is considered. Necessary and sufficient conditions are established for the existence of output feedbacks such that the closed-loop system is regular, has index at most one and \(E+ BG\Gamma\) has a desired rank. Numerial procedures based on orthogonal matrix transformations for construction of the desired feedback gains are derived.