Approximation of the joint spectral radius using sum of squares
| dc.creator | Parrilo, Pablo A. | |
| dc.creator | Jadbabaie, Ali | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T09:27:46Z | |
| dc.date.available | 2026-07-07T09:27:46Z | |
| dc.description | 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. | |
| dc.description | 18 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0712.2887 | |
| dc.identifier | http://arxiv.org/abs/0712.2887 | |
| dc.identifier | Linear Algebra and its Applications, Vol. 428, No. 10, pp. 2385-2402, 2008. | |
| dc.identifier | doi:10.1016/j.laa.2007.12.027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157220 | |
| dc.subject | Optimization and Control | |
| dc.title | Approximation of the joint spectral radius using sum of squares | |
| dc.type | text |