Approximation of the joint spectral radius using sum of squares

Details Approximation of the joint spectral radius using sum of squares Approximation of the joint spectral radius using sum of squares

2007-12-18

arxiv.org/abs/0712.2887v1

Linear Algebra and its Applications, Vol. 428, No. 10, pp. 2385-2402, 2008.

Mathematics

Optimization and Control

18 pages, 1 figure

Scientific paper

10.1016/j.laa.2007.12.027

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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