Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descripto r (generalized state-space) systems by proportional and derivative feedback . We review generalizations of controllability and observability to descrip tor systems along with definitions of regularity and index in terms of the Weierstrass canonical form. Three condensed forms display the controllabili ty and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decis ions, so they may be computed by numerically stable algorithms. In addition , the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/o r proportional output feedback, and, if so, what index can be achieved. Als o included is a a new characterization of descriptor systems that can be ma de to be regular with index 1 by proportional and derivative output feedbac k. (C) 1999 Elsevier Science Inc. All rights reserved.