Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems
We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2013
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| Online Access: | http://hdl.handle.net/1721.1/77224 https://orcid.org/0000-0003-1554-015X |
| _version_ | 1811075993058672640 |
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| author | Amin, Saurabh Hante, Falk M. Bayen, Alexandre M. |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Amin, Saurabh Hante, Falk M. Bayen, Alexandre M. |
| author_sort | Amin, Saurabh |
| collection | MIT |
| description | We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching. We also provide an explicit dwell-time bound for guaranteeing exponential stability of the switching system when, for each mode, the system is exponentially stable. Our stability conditions only depend on the system parameters and boundary data. These conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption. We present tutorial examples to illustrate the instabilities that can result from switching. |
| first_indexed | 2024-09-23T10:14:29Z |
| format | Article |
| id | mit-1721.1/77224 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:14:29Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/772242022-09-26T16:39:32Z Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems Amin, Saurabh Hante, Falk M. Bayen, Alexandre M. Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Amin, Saurabh We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching. We also provide an explicit dwell-time bound for guaranteeing exponential stability of the switching system when, for each mode, the system is exponentially stable. Our stability conditions only depend on the system parameters and boundary data. These conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption. We present tutorial examples to illustrate the instabilities that can result from switching. 2013-02-27T20:17:59Z 2013-02-27T20:17:59Z 2011-05 2010-09 Article http://purl.org/eprint/type/JournalArticle 0018-9286 http://hdl.handle.net/1721.1/77224 Amin, S., F. M. Hante, and A. M. Bayen. “Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems.” IEEE Transactions on Automatic Control 57.2 (2012): 291–301. https://orcid.org/0000-0003-1554-015X en_US http://dx.doi.org/10.1109/tac.2011.2158171 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Other University Web Domain |
| spellingShingle | Amin, Saurabh Hante, Falk M. Bayen, Alexandre M. Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title | Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title_full | Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title_fullStr | Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title_full_unstemmed | Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title_short | Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems |
| title_sort | exponential stability of switched linear hyperbolic initial boundary value problems |
| url | http://hdl.handle.net/1721.1/77224 https://orcid.org/0000-0003-1554-015X |
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