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arXiv · 0712.2887

Approximation of the joint spectral radius using sum of squares

Pablo A. Parrilo·Ali Jadbabaie
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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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Pablo A. Parrilo, Ali Jadbabaie. 2007-12-18. Approximation of the joint spectral radius using sum of squares. https://doi.org/10.1016/j.laa.2007.12.027

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