Lab Papers (GRASP)

Document Type

Journal Article

Date of this Version



Copyright 2008 Elsevier.
Reprinted from:
Pablo A. Parrilo, Ali Jadbabaie, Approximation of the joint spectral radius using sum of squares, Linear Algebra and its Applications, Volume 428, Issue 10, Special Issue on the Joint Spectral Radius: Theory, Methods and Applications, 1 May 2008, Pages 2385-2402, ISSN 0024-3795
DOI: 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.


Joint spectral radius, Sum of squares programming, Lyapunov function, Matrix lifting



Date Posted: 23 September 2009

This document has been peer reviewed.