DESCRIPTOR SYSTEMS WITHOUT CONTROLLABILITY AT INFINITY

This paper concerns the structure that can be achieved by feedback in descriptor systems that lack controllability at infinity. Staircase an d double staircase condensed forms obtained through a sequence of orth ogonal state transformations display when and how feedback can be used to achieve minimal index. Furthermore, they reveal that the modes tha t are uncontrollable at infinity have a fixed minimal index that canno t be reduced by feedback. However, this fixed higher index part of the control system is constrained to be zero in an appropriate coordinate system, provided the initial conditions are consistent. The remainder is a reduced order system that is controllable at infinity that can b e made to have index one by feedback.