DEFLATION IN EIGENVALUE ASSIGNMENT OF DESCRIPTOR SYSTEMS USING STATE-FEEDBACK

The idea of deflation by unitary equivalence transformations has been shown to be very efficient when it is applied to eigen-related problems. In this paper, we show how this kind of deflation may be used to solve the eigenvalue assignment problem for descriptor systems using state feedback. We first transform the system to a form that reveals its controllability. The uncontrollable part of the system, if any, is then discarded and we continue the assignments with the completely controllable part of the system. In order to give the required insight to the approach, we first derive a ''mathematical'' method for the solution of the above problem, without considering numerical issues. This is performed using the idea of deflation. We then show how this method can be modified to derive a numerically efficient algorithm. The significance of presenting our results in the above way rather than getting into the efficient algorithm immediately, is that a similar ''mathematical'' method may easily be used to solve other eigenassignment problems. From this method then, a numerically efficient algorithm may be derived. Being able however, to derive the efficient algorithm directly, ignoring its origin may be quite difficult and rather mystifying, especially to the nonspecialist. The numerical stability of the efficient algorithm is proven, and a numerical example is also presented.