Lecture 7 - Notes

January 19th, 2016

Term	Definition
Node	Point representing a variable or a signal
Source	A node without incoming branches (input node)
Sink	A node with incoming branches only (output nodes)
Mixed Node	Both incoming and outgoing nodes
Path	Connected branches in the direction of the branch arrows. If a node is crossed more than once it is closed
Forward Path	From input node to output node without crossing nodes more than once
Loop	Closed path
Non touching loops	Loops that do not possess common nodes

Properties of Signal Flow Graphs

1. A branch indicates the functional dependence of one signal on another. A signal passes through each branch that is connected
2. A node adds the signals of all incoming branches and transmits this sum to all outgoing branches
3. A mixed node with both incoming and outgoing branches can be treated as a sink by adding an outgoing branch of unity transmittance. But you cannot change a mixed node to a source by this method.
4. For a given system the signal flow graph is not unique

Mason's Formula

$$p = \frac{1}{\Delta} \sum_{k} P_{k} \Delta_{k}$$

State-Space Description

• TODO

Canonical State-Space Representations of Continuous Systems

• TODO