This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# SystemsModelSeriesConnect

 SystemsModelSeriesConnect connects TransferFunctionModel or StateSpaceModel objects and in series. SystemsModelSeriesConnect connects only output y of to input u of . SystemsModelSeriesConnect connects outputs of to inputs of .
• The inputs and outputs of the system produced by SystemsModelSeriesConnect are the inputs of and the outputs of , respectively.
• The arguments y, u, , and are integers specifying the positions of the input or output channels.
• If or is in state-space form, the result is given in state-space form.
Connect two systems in series:
Connect three discrete-time systems in series:
Connect the second output of a two-output system to a single-input system:
Connect two state-space models in series:
Connect the second output of the first system to the first input of the second system:
Connect the inputs to the outputs in reverse order:
Connect two systems in series:
 Out[1]=

Connect three discrete-time systems in series:
 Out[1]=

Connect the second output of a two-output system to a single-input system:
 Out[1]=

Connect two state-space models in series:
 Out[1]=
Connect the second output of the first system to the first input of the second system:
 Out[2]=
Connect the inputs to the outputs in reverse order:
 Out[3]=
 Scope   (3)
Connect two single-input, single-output systems in series:
Connect a system with two outputs to a system with two inputs:
Connect the first output to the second input:
Connect the first and second outputs of the first system to the second and first inputs of the second system:
Connect the two outputs of the first system to the first two inputs of the second system:
Connect the second output to the fourth input:
Connect the first output to the first and third inputs:
 Applications   (4)
A function that connects any number of matching systems in series:
Connect a family of first-order systems in series:
Connect several multiple-input, multiple-output systems:
The cascade of four abstract systems:
The tree structure of the cascade:
Obtain the open-loop transfer function of an azimuth-positioning system having a power amplifier, motor-load, and angular rate sensor in series:
Visualize the open-loop step response:
Integrate the last output of a three-output system:
Use SystemsModelSeriesConnect in multi-loop reduction:
SystemsModelSeriesConnect yields a system that has the inputs of the first system and the outputs of the second system:
SystemsModelSeriesConnect does not cancel poles and zeros:
The poles of the reduced system containing only series and parallel connections are the poles of the individual subsystems:
The order of the reduced system is the sum of the orders of the subsystems:
SystemsModelSeriesConnect is essentially a flat function:
SystemsModelSeriesConnect is essentially equivalent to TransferFunctionModel without any pole-zero cancellation:
For continuous-time systems, SystemsModelSeriesConnect is essentially the Laplace transform of the convolution of the impulse responses:
If any one of the subsystems is a StateSpaceModel object, so is the result:
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