A note on stability conditions for planar switched systems
| dc.creator | Balde, Moussa | |
| dc.creator | Boscain, Ugo | |
| dc.creator | Mason, Paolo | |
| dc.date | 2008-09-22 | |
| dc.date | 2008-09-24 | |
| dc.date.accessioned | 2026-07-07T10:04:34Z | |
| dc.date.available | 2026-07-07T10:04:34Z | |
| dc.description | This paper is concerned with the stability problem for the planar linear switched system $\dot x(t)=u(t)A_1x(t)+(1-u(t))A_2x(t)$, where the real matrices $A_1,A_2\in \R^{2\times 2}$ are Hurwitz and $u(\cdot) [0,\infty[\to\{0,1\}$ is a measurable function. We give coordinate-invariant necessary and sufficient conditions on $A_1$ and $A_2$ under which the system is asymptotically stable for arbitrary switching functions $u(\cdot)$. The new conditions unify those given in previous papers and are simpler to be verified since we are reduced to study 4 cases instead of 20. Most of the cases are analyzed in terms of the function $Γ(A_1,A_2)={1/2}(\tr(A_1) \tr(A_2)- \tr(A_1A_2))$. | |
| dc.description | 9 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0809.3768 | |
| dc.identifier | http://arxiv.org/abs/0809.3768 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169723 | |
| dc.subject | Optimization and Control | |
| dc.title | A note on stability conditions for planar switched systems | |
| dc.type | text |