Numerical Methods for the Regularizationof Descriptor Systems by Output

Conditions are given under which a descriptor, or generalized state-space, system can be regularized by output feedback. It is shown that under these conditions proportional and derivative output feedback controls can be constructed such that the closed loop system is regular and has index at most 1. This property ensures the solvability of the resulting system of dynamicalgebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way.