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OutputControllableModelQ[ssm]

gives True if the state-space model ssm is output controllable, and False otherwise.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
Related Guides
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OutputControllableModelQ

OutputControllableModelQ[ssm]

gives True if the state-space model ssm is output controllable, and False otherwise.

Details and Options

  • The StateSpaceModel ssm is said to be completely output controllable if, for any initial time and any initial state, there exists some control input that drives the output to any desired final value in finite time.
  • The model ssm can either be a standard or descriptor StateSpaceModel.

Examples

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Basic Examples  (2)

An output-controllable system:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{-1, 2, 3}, {2, 1, -1}, {1, 0, 2}}, {{1}, {0}, {-1}}, {{1, -1, 0}, {1, 0, -1}}, {{0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

A system that is not output-controllable:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{1, 1}, {-1, -2}}, {{1}, {-1}}, {{2, 0}, {1, 0}}, {{0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

Scope  (4)

Test if a continuous-time system is output-controllable:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{1, -1, 1}, {1, 2, 1}, {-1, 2, 1}}, {{1}, {0}, {1}}, {{1, 0, 0}, {0, 1, 0}}, {{0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

Test if a discrete-time system is output-controllable:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{0.1, 0.5, 0.1}, {0, 1.4, -0.75}, {0, 1, 0}}, {{0}, {0.35}, {0}}, {{1, 0, 0}}, {{0}}}, SamplingPeriod -> 0.1, SystemsModelLabels -> None]]

A system that is not output-controllable:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{2, 1, 0, 0}, {-2, 0, 1, 0}, {1, 0, 0, 1}, {-0.5, 0, 0, 0}}, {{1}, {-1}, {1}, {0}}, {{1, 1, -1, -1}, {0, 1, -1, 0}, {0.5, 1, -1, -0.5}}, {{0}, {0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

An output-controllable descriptor system:

Wolfram Language code: OutputControllableModelQ[StateSpaceModel[{{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{1}, {0}, {0}, {1}}, {{6, -1, -8, -18}}, {{0}}, {{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, 0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

Properties & Relations  (1)

Controllability and output-controllability are not correlated:

Wolfram Language code: ssm = StateSpaceModel[{{{-2, 0, 0}, {0, 0, 0}, {0, 0, -3}}, {{1}, {0}, {1}}, {{1, 0, 0}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]; {OutputControllableModelQ[ssm], ControllableModelQ[ssm]}
Wolfram Research (2010), OutputControllableModelQ, Wolfram Language function, https://reference.wolfram.com/language/ref/OutputControllableModelQ.html (updated 2012).

Text

Wolfram Research (2010), OutputControllableModelQ, Wolfram Language function, https://reference.wolfram.com/language/ref/OutputControllableModelQ.html (updated 2012).

CMS

Wolfram Language. 2010. "OutputControllableModelQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/OutputControllableModelQ.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_outputcontrollablemodelq, author="Wolfram Research", title="{OutputControllableModelQ}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/OutputControllableModelQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_outputcontrollablemodelq, organization={Wolfram Research}, title={OutputControllableModelQ}, year={2012}, url={https://reference.wolfram.com/language/ref/OutputControllableModelQ.html}, note=[Accessed: 13-June-2026]}