Limits of state feedback in linear systems

Considers the limits of static state feedback in altering the eigenstructure of linear descriptor systems. The fundamental theorem given identifies the limits of state feedback in altering the eigenstructure of system as follows. The total number of eigenvalues assignable is limited from below by the proper controllability indices. The eigenvalues can be chosen at will but the chains of multiple eigenvalues are limited in size from below by the controllability indices. In addition, the presence of infinite zeros limits the number of infinite eigenvalue chains.