Signal flow graphs of sampled-data systems: A new formulation

The pictorial representation of either continuous or discrete systems accomplished by the signal flow-graph technique is extended to mixed discrete-continuous (hybrid) systems. A new flow-graph symbol is introduced in order to distinguish between continuous and discrete variables as well as to indicate the operation of sampling. For the case of linear, time-invariant systems, the algebra for manipulation of such graphs is given. It is shown that the input-output relations of the system are related to certain topological properties of the corresponding signal flow graph. This relation is established and illustrated by several examples. In the case of continuous (or completely discrete) systems, it is shown that the general input-output relation reduces to Mason's formula.