connects systems models sys1 and sys2 in series.


connects outputs out1i of sys1 to inputs in2i of sys2.



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Basic Examples  (4)

Connect two continuous-time systems in series:

Connect two discrete-time systems in series:

Connect state-space systems:

Connect the second output from the first system to the first input of the second system:

Scope  (13)

Basic Uses  (5)

Connect scalar systems:

Connect multivariable systems:

Connect the second output from the first system to the first input of the second system:

Connect discrete-time systems:

Connect a StateSpaceModel to a TransferFunctionModel:

System Types  (8)

Connect two TransferFunctionModel systems:

With delays:

Using improper transfer functions:

Connect two StateSpaceModel systems:

With delays:

Using descriptor state-space models:

Input linear AffineStateSpaceModel systems:

General nonlinear NonlinearStateSpaceModel systems:

Connecting a transfer function and a state-space model will give a state-space model:

Reversing the order gives an equivalent state-space model:

They give the same transfer functions:

Connection with delays:

Connecting a standard linear system and an input linear system will give an affine model:

Connecting a linear or affine system with a nonlinear system gives a nonlinear model:

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:

Create a positioning system with a power amplifier, motor, 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:

Properties & Relations  (8)

The resulting system has the inputs of the first system and the outputs of the second system:

SystemsModelSeriesConnect is a special case of SystemsConnectionsModel:

SystemsModelSeriesConnect does not cancel poles and zeros:

A system made from series and parallel connections has the same poles as the subsystems:

The order of the reduced system is the sum of the orders of the subsystems:

SystemsModelSeriesConnect is essentially a flat function:

Series connections are equivalent to multiplication without any pole-zero cancellation:

Take the Laplace transform of the convolution of two impulse responses:

A series connection gives the same result:

Possible Issues  (1)

Multiple outputs of sys1 cannot be connected to a single input of sys2:

Wolfram Research (2010), SystemsModelSeriesConnect, Wolfram Language function, (updated 2014).


Wolfram Research (2010), SystemsModelSeriesConnect, Wolfram Language function, (updated 2014).


Wolfram Language. 2010. "SystemsModelSeriesConnect." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.


Wolfram Language. (2010). SystemsModelSeriesConnect. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_systemsmodelseriesconnect, author="Wolfram Research", title="{SystemsModelSeriesConnect}", year="2014", howpublished="\url{}", note=[Accessed: 13-July-2024 ]}


@online{reference.wolfram_2024_systemsmodelseriesconnect, organization={Wolfram Research}, title={SystemsModelSeriesConnect}, year={2014}, url={}, note=[Accessed: 13-July-2024 ]}