# SystemsModelStateFeedbackConnect

SystemsModelStateFeedbackConnect[sys,con]

connects the states of the systems model sys to the controller con and the outputs of con to the inputs of sys in feedback.

SystemsModelStateFeedbackConnect[sys,con,{s1,},{{in1,ftype1},}]

connects state si of sys to the i input of con and the j output of con to input inj of sys with feedback type ftypej

# Examples

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## Basic Examples(3)

Determine the closed-loop model of a state-feedback system:

Compute the feedback gains to place the poles at z1 and z2 for a discrete-time system:

Determine the closed-loop model:

Verify the pole locations:

Determine the closed-loop model with a set of optimal state feedback gains:

## Scope(15)

### Basic Uses(10)

The closed-loop model of a system with state feedback:

With positive state feedback:

The state feedback gains specified as a transfer-function model:

The gains specified as a state-space model:

A affine state-space model with feedback specified in a vector:

A nonlinear state-space model with feedback specified in a vector:

Positive state feedback:

Only feedback to the first input:

Only feedback to the second input:

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

The closed-loop model of a multiple-input system:

### System Types(5)

Connect two StateSpaceModel systems:

With delays:

Using descriptor state-space models:

Input linear AffineStateSpaceModel systems:

General nonlinear NonlinearStateSpaceModel systems:

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:

## Applications(3)

The linearized inverted pendulum model is unstable:

Calculate a gain matrix to place the closed-loop poles in the left half-plane:

Find the closed-loop system:

The closed-loop response is stable:

Calculate a gain matrix to optimize a quadratic cost function of the input and the states:

Find the closed-loop system:

Calculate a gain matrix to optimize a quadratic cost function of the input and the outputs:

Find the closed-loop system:

## Properties & Relations(1)

A model where the output matrix is identity and the direct transmission matrix is zero:

SystemsModelStateFeedbackConnect and SystemsModelFeedbackConnect are equivalent:

Wolfram Research (2010), SystemsModelStateFeedbackConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html (updated 2014).

#### Text

Wolfram Research (2010), SystemsModelStateFeedbackConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html (updated 2014).

#### CMS

Wolfram Language. 2010. "SystemsModelStateFeedbackConnect." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html.

#### APA

Wolfram Language. (2010). SystemsModelStateFeedbackConnect. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html

#### BibTeX

@misc{reference.wolfram_2022_systemsmodelstatefeedbackconnect, author="Wolfram Research", title="{SystemsModelStateFeedbackConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html}", note=[Accessed: 28-January-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_systemsmodelstatefeedbackconnect, organization={Wolfram Research}, title={SystemsModelStateFeedbackConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html}, note=[Accessed: 28-January-2023 ]}