connects the outputs from sys to the inputs with negative feedback.


only feedback connect the outputs and inputs in coni.


connects the outputs of sys1 to sys2 and the outputs of sys2 to the inputs of sys1 in feedback.


connects output outi of sys1 to the i^(th) input of sys2 and the j^(th) output of sys2 to input inj of sys1 with feedback type ftypej.


  • The systems model sysi can be a TransferFunctionModel, StateSpaceModel, AffineStateSpaceModel, or NonlinearStateSpaceModel.
  • Connections coni can be given as:
  • {out,in}connect output out to input in in negative feedback
    {out,in,ftype}use positive or negative feedback type ftype
  • By default, sys2 is a unity gain system.
  • The arguments in, out, ini, and outi are integers specifying the positions of the input or output channels.
  • The ftype can be specified as "Negative" or -1 for negative feedback, and "Positive" or 1 for positive feedback. The default type is "Negative".


open allclose all

Basic Examples  (6)

A transfer function with negative unity feedback:

Connect two continuous-time systems in negative feedback:

Connect two discrete-time systems in negative feedback:

A state-space system with negative feedback:

Connect two state-space systems:

Feedback the second output to the first input:

Scope  (18)

Basic Uses  (10)

A unity negative feedback system:

A positive feedback system:

Connect two scalar systems:

Connect multivariable systems:

Connect the second output to the first input:

Connect the second output to the first input through a feedback system:

Connect discrete-time systems:

Connect two systems in positive feedback:

Connect two state-space models as shown in the diagram:

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 state-space model will give a state-space model:

Connection with delays:

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

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

Generalizations & Extensions  (2)

Use one feedback type for all connections:

Connect two systems with positive feedback:

Applications  (5)

Obtain the closed-loop transfer function of a discrete-time system with an integral controller and feedback sensor:

A motor-load servo system with position and velocity feedback:

With only position feedback, the system is unstable:

The closed-loop system, with rate feedback in the inner loop and position feedback in the outer loop:

The response to a unit step:

Use SystemsModelFeedbackConnect in multi-loop reduction:

Compute the complementary sensitivity function from the loop transfer function:

A crankshaft receives a delayed input signal from the engine controller:

Including a simple controller shows the delay is internal to the closed-loop system:

Properties & Relations  (3)

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

SystemsModelFeedbackConnect is a special case of SystemsConnectionsModel:

Connect two transfer functions tfm1 and tfm2:

This is equivalent to (IdentityMatrix[n]+tfm1.tfm2)-1.tfm1:

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


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


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


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


@misc{reference.wolfram_2024_systemsmodelfeedbackconnect, author="Wolfram Research", title="{SystemsModelFeedbackConnect}", year="2014", howpublished="\url{}", note=[Accessed: 19-June-2024 ]}


@online{reference.wolfram_2024_systemsmodelfeedbackconnect, organization={Wolfram Research}, title={SystemsModelFeedbackConnect}, year={2014}, url={}, note=[Accessed: 19-June-2024 ]}