Deflation in eigenvalue assignment of descriptor systems using state feedback

It is shown how deflation by unitary equivalence transformations can be used to solve the eigenvalue assignment problem for descriptor systems using state feedback. The system is first transformed to a form that reveals its controllability. The uncontrollable part of the system, if any, is then discarded, and the assignments are continued with the completely controllable part of the system. To give insight into the approach, a mathematical method for the solution is derived, without considering numerical issues, using the idea of deflation. It is shown how this method can be modified to derive a numerically efficient algorithm. The numerical stability of the algorithm is proved and a numerical example is presented