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Approximation of the Joint Spectral Radius of a Set of Matrices Using Sum of Squares

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Hybrid Systems: Computation and Control (HSCC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4416))

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Abstract

We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for a SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and a recent technique due to Blondel and Nesterov, based on lifting of matrices. Theoretical results and numerical investigations show that our approach yields tighter approximations.

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Author information

Authors and Affiliations

  1. Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139,  

    Pablo A. Parrilo

  2. Dept. of Electrical and Systems Engineering and GRASP laboratory, University of Pennsylvania, Philadelphia, PA 19104,  

    Ali Jadbabaie

Authors
  1. Pablo A. Parrilo
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  2. Ali Jadbabaie
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Alberto Bemporad Antonio Bicchi Giorgio Buttazzo

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© 2007 Springer Berlin Heidelberg

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Parrilo, P.A., Jadbabaie, A. (2007). Approximation of the Joint Spectral Radius of a Set of Matrices Using Sum of Squares. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_35

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  • DOI: https://doi.org/10.1007/978-3-540-71493-4_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71492-7

  • Online ISBN: 978-3-540-71493-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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