Algorithms to verify generic causality and controllability of descriptor systems

Graph-theoretic algorithms are developed for determining generic causality and controllability of structured descriptor systems (SDS's). For the case of nonsingular
E
, a completely graph-theoretic characterization of generic controllability of SDS's is developed. The case of singular
E
is partially resolved, with graph-theoretic characterization of necessary conditions and sufficient conditions for generic causality and controllability developed separately. Although not stated explicitly, these results can be easily translated into a graph-theoretic algorithm to test for generic observability of SDS's.