Certifying Unstability of Switched Systems Using Sum of Squares Programming
© 2020 Society for Industrial and Applied Mathematics 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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Society for Industrial & Applied Mathematics (SIAM)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135424 |
| _version_ | 1826189235053395968 |
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| author | Legat, Benoît Parrilo, Pablo Jungers, Raphaël |
| author_facet | Legat, Benoît Parrilo, Pablo Jungers, Raphaël |
| author_sort | Legat, Benoît |
| collection | MIT |
| description | © 2020 Society for Industrial and Applied Mathematics 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 investigate dual formulations for this approach and leverage these dual programs for developing new analysis tools for the JSR. We show that the dual of this convex problem searches for the occupations measures of trajectories with high asymptotic growth rate. We both show how to generate a sequence of guaranteed high asymptotic growth rate and how to detect cases where we can provide lower bounds on the JSR. All results of this paper are presented for the general case of constrained switched systems, that is, systems for which the switching signal is constrained by an automaton. |
| first_indexed | 2024-09-23T08:11:56Z |
| format | Article |
| id | mit-1721.1/135424 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:11:56Z |
| publishDate | 2021 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1354242021-10-28T05:01:29Z Certifying Unstability of Switched Systems Using Sum of Squares Programming Legat, Benoît Parrilo, Pablo Jungers, Raphaël © 2020 Society for Industrial and Applied Mathematics 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 investigate dual formulations for this approach and leverage these dual programs for developing new analysis tools for the JSR. We show that the dual of this convex problem searches for the occupations measures of trajectories with high asymptotic growth rate. We both show how to generate a sequence of guaranteed high asymptotic growth rate and how to detect cases where we can provide lower bounds on the JSR. All results of this paper are presented for the general case of constrained switched systems, that is, systems for which the switching signal is constrained by an automaton. 2021-10-27T20:23:25Z 2021-10-27T20:23:25Z 2020 2021-02-03T16:35:05Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135424 en 10.1137/18M1173460 SIAM Journal on Control and Optimization 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 Society for Industrial & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Legat, Benoît Parrilo, Pablo Jungers, Raphaël Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title | Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title_full | Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title_fullStr | Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title_full_unstemmed | Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title_short | Certifying Unstability of Switched Systems Using Sum of Squares Programming |
| title_sort | certifying unstability of switched systems using sum of squares programming |
| url | https://hdl.handle.net/1721.1/135424 |
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