Graph theoretic methods in the study of structural issues in control

This paper addresses questions regarding controllability and observability for `generic parameter´ dynamical systems. We use graph theoretic methods and hence these questions are answered in a `structural sense´. We formulate necessary and sufficient conditions for controllability in terms of suitable maximum matchings in the bipartite graph constructed from the constraints and variables. The conditions for observability turn out to be similar. We relate these tests to Gilbert´s controllability and observability tests.