Approximation of the joint spectral radius using sum of squares |
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Authors: | Pablo A. Parrilo Ali Jadbabaie |
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Affiliation: | a Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, United States b GRASP Laboratory, University of Pennsylvania, United States |
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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 an 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 earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations. |
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Keywords: | Joint spectral radius Sum of squares programming Lyapunov function Matrix lifting |
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