Stability of Planar Switched Systems: the Nondiagonalizable Case
| dc.creator | Balde, Moussa | |
| dc.creator | Boscain, Ugo | |
| dc.date | 2006-10-12 | |
| dc.date.accessioned | 2026-07-07T07:29:00Z | |
| dc.date.available | 2026-07-07T07:29:00Z | |
| dc.description | Consider the planar linear switched system $\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where $A$ and $B$ are two $2\times2$ real matrices, $x \in \R^2$, and $u(.):[0,\infty[\to\{0,1\}$ is a measurable function. In this paper we consider the problem of finding a (coordinate-invariant) necessary and sufficient condition on $A$ and $B$ under which the system is asymptotically stable for arbitrary switching functions $u(.)$. This problem was solved in previous works under the assumption that both $A$ and $B$ are diagonalizable. In this paper we conclude this study, by providing a necessary and sufficient condition for asymptotic stability in the case in which $A$ and/or $B$ are not diagonalizable. To this purpose we build suitable normal forms for $A$ and $B$ containing coordinate invariant parameters. A necessary and sufficient condition is then found without looking for a common Lyapunov function but using "worst-trajectory'' type arguments. | |
| dc.identifier | https://arxiv.org/abs/math/0610401 | |
| dc.identifier | http://arxiv.org/abs/math/0610401 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117942 | |
| dc.subject | Optimization and Control | |
| dc.subject | 93D20, 37N35 | |
| dc.title | Stability of Planar Switched Systems: the Nondiagonalizable Case | |
| dc.type | text |