Eigenstructure assignment in linear descriptor systems

Given a linear controllable system Ex/spl dot/=Fx+Gu, we study the limits of linear proportional feedback u=Kx+/spl upsi/ in assigning a desired finite and infinite eigenstructure of the closed-loop system Ex/spl dot/=(F+GK)x+G/spl upsi/. The closed-loop system is not restricted to be regular; its rank makes part of the specifications. Necessary and sufficient conditions are established for the existence of a feedback gain K which assigns the desired eigenstructure, and a procedure is outlined to calculate one such gain.