An entropy-based bound for the computational complexity of a switched system
© 2019 IEEE. The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the st...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/136543 |
| _version_ | 1811076805592875008 |
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| author | Legat, Benoit Parrilo, Pablo A Jungers, Raphael M |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Legat, Benoit Parrilo, Pablo A Jungers, Raphael M |
| author_sort | Legat, Benoit |
| collection | MIT |
| description | © 2019 IEEE. The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyze the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the $p$-radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low-rank matrices to the computation of the constrained JSR of matrices of small dimension. |
| first_indexed | 2024-09-23T10:27:52Z |
| format | Article |
| id | mit-1721.1/136543 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:27:52Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1365432023-02-17T19:15:24Z An entropy-based bound for the computational complexity of a switched system Legat, Benoit Parrilo, Pablo A Jungers, Raphael M Massachusetts Institute of Technology. Laboratory for Information and Decision Systems © 2019 IEEE. The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyze the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the $p$-radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low-rank matrices to the computation of the constrained JSR of matrices of small dimension. 2021-10-27T20:35:51Z 2021-10-27T20:35:51Z 2019 2021-02-03T16:11:48Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136543 en 10.1109/TAC.2019.2902625 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Legat, Benoit Parrilo, Pablo A Jungers, Raphael M An entropy-based bound for the computational complexity of a switched system |
| title | An entropy-based bound for the computational complexity of a switched system |
| title_full | An entropy-based bound for the computational complexity of a switched system |
| title_fullStr | An entropy-based bound for the computational complexity of a switched system |
| title_full_unstemmed | An entropy-based bound for the computational complexity of a switched system |
| title_short | An entropy-based bound for the computational complexity of a switched system |
| title_sort | entropy based bound for the computational complexity of a switched system |
| url | https://hdl.handle.net/1721.1/136543 |
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