Emgr - Revision history

Himpe: /* References */ Add TOMS paper

2024-01-11T21:34:50Z

References: Add TOMS paper

← Older revision		Revision as of 21:34, 11 January 2024
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	== References ==		== References ==

			* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1145/3609860 emgr - EMpirical GRamian Framework 5.99]</span>". Transactions on Mathematical Software, 49(3): 31, 2023.

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_7 Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_7 Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.

Himpe: emgr 5.99 update

2022-04-13T12:52:16Z

emgr 5.99 update

← Older revision		Revision as of 12:52, 13 April 2022
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	== Synopsis ==		== Synopsis ==

	[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.9''').		[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.99''').
	Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.		Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.
	Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.		Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.
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	\|-		\|-
	\|style="text-align:right;" \| '''version:'''		\|style="text-align:right;" \| '''version:'''
	\|5.9 (~~2021~~-21-01)		\|5.99 (2022-04-13)
	\|-		\|-
	\|style="text-align:right;" \| '''id:'''		\|style="text-align:right;" \| '''id:'''
	\|[https://doi.org/10.5281/zenodo.~~4454679~~ 10.5281/zenodo.~~4454679~~] (doi)		\|[https://doi.org/10.5281/zenodo.6457616 10.5281/zenodo.6457616] (doi)
	\|-		\|-
	\|style="text-align:right;" \| '''author:'''		\|style="text-align:right;" \| '''author:'''
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	Please cite '''emgr''' as:		Please cite '''emgr''' as:

	C. Himpe (2021). emgr - EMpirical GRamian Framework (Version 5.9) [Software].		C. Himpe (2021). emgr - EMpirical GRamian Framework (Version 5.99) [Software].
	Available from https://gramian.de . doi:10.5281/zenodo.~~4454679~~		Available from https://gramian.de . doi:10.5281/zenodo.6457616

	@MISC{~~emgr59~~,		@MISC{emgr599,
	author = {C.~Himpe},		author = {C.~Himpe},
	title = {{emgr - {EMpirical GRamian Framework} (Version~5.9)},		title = {{emgr - {EMpirical GRamian Framework} (Version~5.99)},
	howpublished = {\url{https://gramian.de}},		howpublished = {\url{https://gramian.de}},
	year = {~~2021~~},		year = {2022},
	doi = {10.5281/zenodo.~~4454679~~}		doi = {10.5281/zenodo.6457616}
	}		}

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	* Official website: https://gramian.de		* Official website: https://gramian.de

			* Github Repo: https://github.com/gramian/emgr

			* SWmath: [https://swmath.org/software/7554 Entry]

	* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]		* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]

Himpe: /* References */ Updated

2021-08-26T07:17:31Z

References: Updated

← Older revision		Revision as of 07:17, 26 August 2021
Line 111:		Line 111:
	== References ==		== References ==

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2002.12226~~ Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". ~~arXiv~~, ~~math.OC~~: ~~2002.12226~~, ~~2020~~.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_7 Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.

	* P. Benner, [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/s10444-019-09724-7 Cross-Gramian-Based Dominant Subspaces]</span>". Advances in Computational Mathematics 45(5): 91, 2533--2553, 2019.		* P. Benner, [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/s10444-019-09724-7 Cross-Gramian-Based Dominant Subspaces]</span>". Advances in Computational Mathematics 45(5): 91, 2533--2553, 2019.

Himpe: emgr 5.9

2021-01-21T15:25:20Z

emgr 5.9

← Older revision		Revision as of 15:25, 21 January 2021
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	== Synopsis ==		== Synopsis ==

	[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.8''').		[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.9''').
	Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.		Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.
	Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.		Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.
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	** Balanced Truncation		** Balanced Truncation
	** Balanced Gains		** Balanced Gains
			** Dynamic Mode Decomposition-Galerkin
	* Parameter reduction		* Parameter reduction
	* Combined state and parameter reduction		* Combined state and parameter reduction
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	\|-		\|-
	\|style="text-align:right;" \| '''version:'''		\|style="text-align:right;" \| '''version:'''
	\|5.8 (~~2020~~-05-01)		\|5.9 (2021-21-01)
	\|-		\|-
	\|style="text-align:right;" \| '''id:'''		\|style="text-align:right;" \| '''id:'''
	\|[https://doi.org/10.5281/zenodo.~~3779889~~ 10.5281/zenodo.~~3779889~~] (doi)		\|[https://doi.org/10.5281/zenodo.4454679 10.5281/zenodo.4454679] (doi)
	\|-		\|-
	\|style="text-align:right;" \| '''author:'''		\|style="text-align:right;" \| '''author:'''
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	Please cite '''emgr''' as:		Please cite '''emgr''' as:

	C. Himpe (~~2020~~). emgr - EMpirical GRamian Framework (Version 5.8) [Software].		C. Himpe (2021). emgr - EMpirical GRamian Framework (Version 5.9) [Software].
	Available from https://gramian.de . doi:10.5281/zenodo.~~3779889~~		Available from https://gramian.de . doi:10.5281/zenodo.4454679

	@MISC{~~emgr58~~,		@MISC{emgr59,
	author = {C. Himpe},		author = {C.~Himpe},
	title = {{emgr -{EMpirical GRamian Framework} (Version~5.8)},		title = {{emgr - {EMpirical GRamian Framework} (Version~5.9)},
	howpublished = {\url{https://gramian.de}},		howpublished = {\url{https://gramian.de}},
	year = {~~2020~~},		year = {2021},
	doi = {10.5281/zenodo.~~3779889~~}		doi = {10.5281/zenodo.4454679}
	}		}

Himpe: add citation, refs, and update scope

2020-10-22T13:59:52Z

add citation, refs, and update scope

← Older revision		Revision as of 13:59, 22 October 2020
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	'''emgr''' encompasses seven types of gramians:		'''emgr''' encompasses seven types of gramians:

	* Empirical [[:Wikipedia:Controllability_Gramian\|Controllability Gramian]]		* Empirical [[:Wikipedia:Controllability_Gramian\|Controllability Gramian]] / Empirical Output Controllability Gramian
	* Empirical [[:Wikipedia:Observability_Gramian\|Observability Gramian]]		* Empirical [[:Wikipedia:Observability_Gramian\|Observability Gramian]] / Empirical Average Observability Gramian
	* Empirical [[:Wikipedia:Cross_Gramian\|Cross Gramian]] ~~(including an~~ Empirical Non-Symmetric Cross Gramian)		* Empirical [[:Wikipedia:Cross_Gramian\|Cross Gramian]] / Empirical Non-Symmetric Cross Gramian
	* Empirical Linear ~~[[:Wikipedia:Cross_Gramian\|~~Cross Gramian]]		* Empirical Linear Cross Gramian / Empirical Non-Symmetric Linear Cross Gramian
	* Empirical Sensitivity Gramian (parameter controllability)		* Empirical Sensitivity Gramian (parameter controllability)
	* Empirical Identifiability Gramian (parameter observability)		* Empirical Identifiability Gramian (parameter observability)
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	[[File:emgr-flyer.pdf\|thumb\|right\|emgr overview]]		[[File:emgr-flyer.pdf\|thumb\|right\|emgr overview]]

	~~applicable to~~:		=== Applications: ===

	* ~~Linear + Nonlinear Control Systems~~		* Model reduction
	* ~~First + Second Order Control Systems~~		** Proper Orthogonal Decomposition (POD)
	* ~~Parametrized \| Parametric Systems~~		** Modified POD / Approximate Balancing
	* ~~Time Invariant + Varying Systems~~		** Dominant Subspace Projection Model Reduction (DSPMR)
	* ~~Discretized [[:Wikipedia:Partial_differential_equation\|PDEs]]~~		** Balanced Proper Orthogonal Decompsition (bPOD)
			** Balanced Truncation
	~~and with sample code for:~~		** Balanced Gains
			* Parameter reduction
	* ~~[[Balanced Truncation]]~~ and ~~balancing related methods~~		* Combined state and parameter reduction
	* ~~Combined~~ State ~~and~~ Parameter ~~Reduction~~		* Decentralized control
	* Parameter ~~Identification + Sensitivity Analysis~~		* State sensitivity
	* ~~Parameter Reduction + Robust Reduction~~		* Parameter sensitivity
	* ~~Optimal Sensor + Actuator Placement~~		* Parameter identification
	* ~~Decentralized Control~~		* Nonlinearity quantification
	* ~~Nonlinearity Quantification~~		* Uncertainty quantification
			* System indices
			* System norms
			* Tau function

	== Meta Information ==		== Meta Information ==
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	\|Controllability, Observability, Cross Gramian, Model Reduction, Model Order Reduction		\|Controllability, Observability, Cross Gramian, Model Reduction, Model Order Reduction
	\|}		\|}

			== Cite ==

			Please cite '''emgr''' as:

			C. Himpe (2020). emgr - EMpirical GRamian Framework (Version 5.8) [Software].
			Available from https://gramian.de . doi:10.5281/zenodo.3779889

			@MISC{emgr58,
			author = {C. Himpe},
			title = {{emgr -{EMpirical GRamian Framework} (Version~5.8)},
			howpublished = {\url{https://gramian.de}},
			year = {2020},
			doi = {10.5281/zenodo.3779889}
			}

	== References ==		== References ==

			* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://arxiv.org/abs/2002.12226 Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". arXiv, math.OC: 2002.12226, 2020.

			* P. Benner, [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/s10444-019-09724-7 Cross-Gramian-Based Dominant Subspaces]</span>". Advances in Computational Mathematics 45(5): 91, 2533--2553, 2019.

	* S. Grundel, [[User:Himpe\|C. Himpe]], J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201900006 On Empirical System Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.		* S. Grundel, [[User:Himpe\|C. Himpe]], J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201900006 On Empirical System Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.
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	* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]		* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]

	* DSweb Dynamical Systems Software: [https://dsweb.siam.org/Software/emgr-empirical-gramian-framework Entry]		* SIAM DSweb Dynamical Systems Software: [https://dsweb.siam.org/Software/emgr-empirical-gramian-framework Entry]

	== Contact ==		== Contact ==

	[[User:Himpe\| Christian Himpe]]		[[User:Himpe\| Christian Himpe]]

Himpe: /* Links */ add DSweb

2020-05-01T11:49:17Z

Links: add DSweb

← Older revision		Revision as of 11:49, 1 May 2020
Line 115:		Line 115:

	* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]		* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]

			* DSweb Dynamical Systems Software: [https://dsweb.siam.org/Software/emgr-empirical-gramian-framework Entry]

	== Contact ==		== Contact ==

	[[User:Himpe\| Christian Himpe]]		[[User:Himpe\| Christian Himpe]]

Himpe: update emgr

2020-05-01T11:47:54Z

update emgr

← Older revision		Revision as of 11:47, 1 May 2020
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	== Synopsis ==		== Synopsis ==

	[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.7''').		[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.8''').
	Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.		Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.
	Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.		Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.
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	\|-		\|-
	\|style="text-align:right;" \| '''version:'''		\|style="text-align:right;" \| '''version:'''
	\|5.7 (~~2019~~-02-26)		\|5.8 (2020-05-01)
	\|-		\|-
	\|style="text-align:right;" \| '''id:'''		\|style="text-align:right;" \| '''id:'''
	\|[https://doi.org/10.5281/zenodo.~~2577980~~ 10.5281/zenodo.~~2577980~~] (doi)		\|[https://doi.org/10.5281/zenodo.3779889 10.5281/zenodo.3779889] (doi)
	\|-		\|-
	\|style="text-align:right;" \| '''author:'''		\|style="text-align:right;" \| '''author:'''
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	\|-		\|-
	\|style="text-align:right;" \| '''dependencies:'''		\|style="text-align:right;" \| '''dependencies:'''
	\|[[wikipedia:GNU_Octave\|Octave]] >=4.2, [[wikipedia:MATLAB\|Matlab]] >=~~2016b~~		\|[[wikipedia:GNU_Octave\|Octave]] >=5.2, [[wikipedia:MATLAB\|Matlab]] >=2017b
	\|-		\|-
	\|style="text-align:right;" \| '''systems:'''		\|style="text-align:right;" \| '''systems:'''

Himpe: /* References */ added PAMM and fixes

2019-11-21T12:25:15Z

References: added PAMM and fixes

← Older revision		Revision as of 12:25, 21 November 2019
Line 91:		Line 91:

	== References ==		== References ==

			* S. Grundel, [[User:Himpe\|C. Himpe]], J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201900006 On Empirical System Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.

	* [[User:Himpe\|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". ~~In:~~ Proceedings in Applied Mathematics and Mechanics, ~~vol.~~ 17~~(1)~~: 841--842, 2017.		* [[User:Himpe\|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 17: 841--842, 2017.

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1080/21642583.2016.1215273 A ~~note~~ on the ~~cross~~ Gramian for ~~non~~-~~symmetric systems~~]</span>". System Science and Control Engineering 4(1): 199--208, 2016.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1080/21642583.2016.1215273 A Note on the Cross Gramian for Non-Symmetric Systems]</span>". System Science and Control Engineering 4(1): 199--208, 2016.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". ~~Proceedings of the~~ 8th Vienna International Conference on Mathematical Modelling 48(1): 727--728, 2015.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". IFAC-PapersOnLine (8th Vienna International Conference on Mathematical Modelling), 48(1): 727--728, 2015.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference ~~2014~~: 2739--2743, 2014.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference: 2739--2743, 2014.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, ~~vol.~~ 2014: 843869, 2014.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, 2014: 843869, 2014.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics 2013: 365909, 2013.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics 2013: 365909, 2013.

Himpe: Added code meta data table.

2019-06-20T13:39:51Z

Added code meta data table.

@@ Line 44: / Line 44: @@
 * Decentralized Control
 * Nonlinearity Quantification
 == References ==
@@ Line 62: / Line 107: @@
 * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics 2013: 365909, 2013.
 == Links ==
 * Official website: https://gramian.de
 * Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]

Himpe: box fix

2019-02-26T14:05:45Z

box fix

← Older revision		Revision as of 14:05, 26 February 2019
Line 3:		Line 3:
	[[Category:Octave]]		[[Category:Octave]]

	[[File:Emgr_box.png\|~~100px~~\|right\|emgr box]]		[[File:Emgr_box.png\|200px\|right\|emgr box]]

	== Synopsis ==		== Synopsis ==

← Older revision		Revision as of 12:25, 21 November 2019
Line 91:		Line 91:

	== References ==		== References ==

			* S. Grundel, [[User:Himpe\|C. Himpe]], J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201900006 On Empirical System Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.

	* [[User:Himpe\|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". ~~In:~~ Proceedings in Applied Mathematics and Mechanics, ~~vol.~~ 17~~(1)~~: 841--842, 2017.		* [[User:Himpe\|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 17: 841--842, 2017.

	* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.		* [[User:Himpe\|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1080/21642583.2016.1215273 A ~~note~~ on the ~~cross~~ Gramian for ~~non~~-~~symmetric systems~~]</span>". System Science and Control Engineering 4(1): 199--208, 2016.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1080/21642583.2016.1215273 A Note on the Cross Gramian for Non-Symmetric Systems]</span>". System Science and Control Engineering 4(1): 199--208, 2016.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". ~~Proceedings of the~~ 8th Vienna International Conference on Mathematical Modelling 48(1): 727--728, 2015.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". IFAC-PapersOnLine (8th Vienna International Conference on Mathematical Modelling), 48(1): 727--728, 2015.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference ~~2014~~: 2739--2743, 2014.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference: 2739--2743, 2014.

	* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, ~~vol.~~ 2014: 843869, 2014.		* [[User:Himpe\|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, 2014: 843869, 2014.

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