Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection
This paper presents theoretical and practical results concerning the stability of piecewise-linear (PWL) reduced models for the purposes of analog macromodeling. Results include proofs of input-output (I/O) stability for PWL approximations to certain classes of nonlinear descriptor systems, along wi...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/52359 https://orcid.org/0000-0002-5880-3151 |
| _version_ | 1811095357417848832 |
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| author | Bond, Bradley N. Daniel, Luca |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Bond, Bradley N. Daniel, Luca |
| author_sort | Bond, Bradley N. |
| collection | MIT |
| description | This paper presents theoretical and practical results concerning the stability of piecewise-linear (PWL) reduced models for the purposes of analog macromodeling. Results include proofs of input-output (I/O) stability for PWL approximations to certain classes of nonlinear descriptor systems, along with projection techniques that are guaranteed to preserve I/O stability in reduced-order PWL models. We also derive a new PWL formulation and introduce a new nonlinear projection, allowing us to extend our stability results to a broader class of nonlinear systems described by models containing nonlinear descriptor functions. Lastly, we present algorithms to compute efficiently the required stabilizing nonlinear left-projection matrix operators. |
| first_indexed | 2024-09-23T16:15:48Z |
| format | Article |
| id | mit-1721.1/52359 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:15:48Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/523592022-09-29T19:12:15Z Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection Bond, Bradley N. Daniel, Luca Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Daniel, Luca Bond, Bradley N. Daniel, Luca stability nonlinear systems model order reduction (MOR) Analog macromodeling This paper presents theoretical and practical results concerning the stability of piecewise-linear (PWL) reduced models for the purposes of analog macromodeling. Results include proofs of input-output (I/O) stability for PWL approximations to certain classes of nonlinear descriptor systems, along with projection techniques that are guaranteed to preserve I/O stability in reduced-order PWL models. We also derive a new PWL formulation and introduce a new nonlinear projection, allowing us to extend our stability results to a broader class of nonlinear systems described by models containing nonlinear descriptor functions. Lastly, we present algorithms to compute efficiently the required stabilizing nonlinear left-projection matrix operators. Interconnect Focus Center 2010-03-05T20:48:15Z 2010-03-05T20:48:15Z 2009-09 2009-04 Article http://purl.org/eprint/type/JournalArticle 0278-0070 http://hdl.handle.net/1721.1/52359 Bond, B.N., and L. Daniel. “Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection.” Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on 28.10 (2009): 1467-1480. © 2009 IEEE https://orcid.org/0000-0002-5880-3151 en_US http://dx.doi.org/10.1109/tcad.2009.2030596 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | stability nonlinear systems model order reduction (MOR) Analog macromodeling Bond, Bradley N. Daniel, Luca Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title | Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title_full | Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title_fullStr | Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title_full_unstemmed | Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title_short | Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection |
| title_sort | stable reduced models for nonlinear descriptor systems through piecewise linear approximation and projection |
| topic | stability nonlinear systems model order reduction (MOR) Analog macromodeling |
| url | http://hdl.handle.net/1721.1/52359 https://orcid.org/0000-0002-5880-3151 |
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