Common Polynomial Lyapunov Functions for Linear Switched Systems
| dc.creator | Mason, Paolo | |
| dc.creator | Boscain, Ugo | |
| dc.creator | Chitour, Yacine | |
| dc.date | 2004-03-12 | |
| dc.date | 2004-08-10 | |
| dc.date.accessioned | 2026-07-07T05:06:20Z | |
| dc.date.available | 2026-07-07T05:06:20Z | |
| dc.description | In this paper, we consider linear switched systems $\dot x(t)=A_{u(t)} x(t)$, $x\in\R^n$, $u\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\bf UAS} for short). We first prove that, given a {\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. | |
| dc.description | 18 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0403209 | |
| dc.identifier | http://arxiv.org/abs/math/0403209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70437 | |
| dc.subject | Optimization and Control | |
| dc.subject | 93D20, 37N35 | |
| dc.title | Common Polynomial Lyapunov Functions for Linear Switched Systems | |
| dc.type | text |