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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.
Joint spectral radius, Sum of squares programming, Lyapunov function, Matrix lifting
Pablo A. Parillo and Ali Jadbabaie, "Approximation of the joint spectral radius using sum of squares", . March 2008.
Date Posted: 23 September 2009
This document has been peer reviewed.