A complete classification of controllable singular systems

A decomposition of the reachable subspace of the singular system Ex´(t)=Ax(t)+Bu(t) into m singly generated reachability subspaces is presented, where E,A,B are real matrices of dimensions n×n, n×n, n×m, respectively. It is not assumed that the system (E,A,B) is regular. This decomposition is used to derive canonical forms for controllable singular systems under the actions of the proportional and proportional-plus-derivative feedback groups