Generic controllability theorems for descriptor systems

This paper presents an extension of the structural controllability theorem to the case of structured descriptor systems (SDS). A major difficulty in this problem is the loss of independence among the entries of the system matrices. This difficulty is resolved by introducing the idea of column structured matrices (CSM). First, the paper defines and characterizes - and -controllability for descriptor systems. Then, the generic controllability theorem is proved, extending the structural controllability theorem to column structured systems (CSS). Finally, based on this result, necessary conditions and sufficient conditions for generic - and -controllability are obtained. The result gives a complete characterization of generic controllability for SDS with nonsingular , and a partial solution for the case of singular .