research-article

Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions

Authors:

Bradley N Bond,

Luca DanielAuthors Info & Claims

ICCAD '07: Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design

Pages 860 - 866

Published: 05 November 2007 Publication History

Get Access

Abstract

In this paper we present several results concerning the stabilization of piecewise-linear reduced order models. We include proofs of internal and external stability for models whose system matrices possess special structures. We then introduce a new projection scheme, and a new set of weighting functions which allow us to extend some of these results to piecewise-linear systems comprised of arbitrary matrices, at least one of which is Hurwitz. Included are an algorithm for creating switching piecewise-linear reduced models comprised of globally exponentially stable systems, and stable simulation results for a system which produces unstable results when using the standard TPWL method.

References

[1]

M. Rewienski and J. White. A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Trans. Computer-Aided Design, 22(2):155--70, Feb 2003.

Digital Library

Google Scholar

[2]

D. Vasilyev, M. Rewienski, and J. White. A tbr-based trajectory piecewise-linear algorithm for generating accurate low-order models for nonlinear analog circuits and mems. In Proc. of the ACM/IEEE Design Automation Conference, pages 490--5, June 2003.

Digital Library

Google Scholar

[3]

N. Dong and J. Roychowdhury. Piecewise polynomial nonlinear model reduction. In Proc. of the ACM/IEEE Design Automation Conference, June 2003.

Digital Library

Google Scholar

[4]

N. Dong and J. Roychowdhury. Automated extraction of broadly applicable nonlinear analog macromodels from spice-level descriptions. In Proc. of the IEEE Custom Integrated Circuits Conference, October 2004.

Crossref

Google Scholar

[5]

S. Tiwary and R. Rutenbar. Scalable trajectory methods for on-demand analog macromodel extraction. In 42 ^nd ACM/IEEE Design Automation Conference, June 2005.

Digital Library

Google Scholar

[6]

N. Dong and J. Roychowdhury. Automated nonlinear macromodelling of output buffers for high-speed digital applications. In 42^nd ACM/IEEE Design Automation Conference, June 2005.

Digital Library

Google Scholar

[7]

B. Bond and L. Daniel. Parameterized model order reduction for nonlinear dynamical systems. In Proc. of the IEEE/ACM International Conference on Computer-Aided Design, pages 487--494, San Jose, CA, 2005.

Digital Library

Google Scholar

[8]

Y. Wan and J. Roychowdhury. Faster, parametric trajectory-based macromodels via localized linear reductions. In Proc. of IEEE/ACM International Conference on Computer Aided-Design, November 2006.

Digital Library

Google Scholar

[9]

M. Rewienski and J. K. White. A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachiend devices. In Proc. of IEEE/ACM International Conference on Computer Aided-Design, pages 252--7, San Jose, CA. USA, November 2001.

Digital Library

Google Scholar

Cited By

View all

Manoj PYu HGu CZhuo CChang Y(2014)A zonotoped macromodeling for reachability verification of eye-diagram in high-speed I/O links with jitterProceedings of the 2014 IEEE/ACM International Conference on Computer-Aided Design10.5555/2691365.2691506(696-701)Online publication date: 3-Nov-2014
https://dl.acm.org/doi/10.5555/2691365.2691506
Song YSai Manoj PYu HFettweis GNebel W(2014)Zonotope-based nonlinear model order reduction for fast performance bound analysis of analog circuits with multiple-interval-valued parameter variationsProceedings of the conference on Design, Automation & Test in Europe10.5555/2616606.2616621(1-6)Online publication date: 24-Mar-2014
https://dl.acm.org/doi/10.5555/2616606.2616621
Gu CRoychowdhury JLin Y(2010)Manifold construction and parameterization for nonlinear manifold-based model reductionProceedings of the 2010 Asia and South Pacific Design Automation Conference10.5555/1899721.1899766(205-210)Online publication date: 18-Jan-2010
https://dl.acm.org/doi/10.5555/1899721.1899766
Show More Cited By

Recommendations

Robust reduced-order l2-l∞ filtering for network-based discrete-time linear systems

This paper investigates the l2-l∞ filtering problem for a class of discrete-time system subject to network-induced delays. The objective is to design a reduced-order filter, such that the estimation errors converge to zero, while an l2-l∞ performance is ...
Finite-time H∞ control of periodic piecewise linear systems

In this paper, the finite-time stability, stabilisation, L₂-gain and H_∞ control problems for a class of continuous-time periodic piecewise linear systems are addressed. By employing a time-varying control scheme in which the time interval of each ...
Stability of impulsive piecewise linear systems

In this article, stability of impulsive piecewise linear systems is investigated and a number of stability criteria are obtained based on Lyapunov functions. Both the stability results that impulses act as perturbation and the stability results that ...

Comments

Information & Contributors

Information

Published In

ICCAD '07: Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design

November 2007

933 pages

ISBN:1424413826

General Chair:
Georges Gielen
ESAT-MICAS, Katholieke Univ. Leuven, Leuven, Belgium

Publisher

IEEE Press

Publication History

Published: 05 November 2007

Check for updates

Qualifiers

Research-article

Conference

ICCAD07

Sponsor:

CEDA
SIGDA
IEEE-CS\DATC

ICCAD07: The International Conference on Computer-Aided Design 2007

November 5 - 8, 2007

California, San Jose

Acceptance Rates

ICCAD '07 Paper Acceptance Rate 139 of 510 submissions, 27%;

Overall Acceptance Rate 457 of 1,762 submissions, 26%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
120
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 17 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Manoj PYu HGu CZhuo CChang Y(2014)A zonotoped macromodeling for reachability verification of eye-diagram in high-speed I/O links with jitterProceedings of the 2014 IEEE/ACM International Conference on Computer-Aided Design10.5555/2691365.2691506(696-701)Online publication date: 3-Nov-2014
https://dl.acm.org/doi/10.5555/2691365.2691506
Song YSai Manoj PYu HFettweis GNebel W(2014)Zonotope-based nonlinear model order reduction for fast performance bound analysis of analog circuits with multiple-interval-valued parameter variationsProceedings of the conference on Design, Automation & Test in Europe10.5555/2616606.2616621(1-6)Online publication date: 24-Mar-2014
https://dl.acm.org/doi/10.5555/2616606.2616621
Gu CRoychowdhury JLin Y(2010)Manifold construction and parameterization for nonlinear manifold-based model reductionProceedings of the 2010 Asia and South Pacific Design Automation Conference10.5555/1899721.1899766(205-210)Online publication date: 18-Jan-2010
https://dl.acm.org/doi/10.5555/1899721.1899766
Cardoso MDurlofsky L(2010)Linearized reduced-order models for subsurface flow simulationJournal of Computational Physics10.1016/j.jcp.2009.10.004229:3(681-700)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.1016/j.jcp.2009.10.004
Gu CRoychowdhury J(2009)QLMORProceedings of the 2009 International Conference on Computer-Aided Design10.1145/1687399.1687474(389-396)Online publication date: 2-Nov-2009
https://dl.acm.org/doi/10.1145/1687399.1687474
Bond BDaniel L(2009)Stable reduced models for nonlinear descriptor systems through piecewise-linear approximation and projectionIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2009.203059628:10(1467-1480)Online publication date: 1-Oct-2009
https://dl.acm.org/doi/10.1109/TCAD.2009.2030596
Bond BDaniel LNassif SRoychowdhury J(2008)Guaranteed stable projection-based model reduction for indefinite and unstable linear systemsProceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design10.5555/1509456.1509615(728-735)Online publication date: 10-Nov-2008
https://dl.acm.org/doi/10.5555/1509456.1509615

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Recommendations

Robust reduced-order l2-l∞ filtering for network-based discrete-time linear systems

Finite-time H∞ control of periodic piecewise linear systems

Stability of impulsive piecewise linear systems

Comments

Published In

Sponsors

Publisher

Publication History

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

Login options

Full Access

PDF

eReader

Abstract

References

Cited By

Recommendations

Robust reduced-order l2-l∞ filtering for network-based discrete-time linear systems

Finite-time H∞ control of periodic piecewise linear systems

Stability of impulsive piecewise linear systems

Comments

Information

Published In

Sponsors

Publisher

Publication History

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

Login options

Full Access

View options

PDF

eReader

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations