On the stabilization of persistently excited linear systems
| dc.creator | Chitour, Yacine | |
| dc.creator | Sigalotti, Mario | |
| dc.date | 2008-10-12 | |
| dc.date | 2009-05-18 | |
| dc.date.accessioned | 2026-07-07T13:15:23Z | |
| dc.date.available | 2026-07-07T13:15:23Z | |
| dc.description | We consider control systems of the type $\dot x = A x +α(t)bu$, where $u\in\R$, $(A,b)$ is a controllable pair and $α$ is an unknown time-varying signal with values in $[0,1]$ satisfying a persistent excitation condition i.e., $\int_t^{t+T}\al(s)ds\geq μ$ for every $t\geq 0$, with $0<μ\leq T$ independent on $t$. We prove that such a system is stabilizable with a linear feedback depending only on the pair $(T,μ)$ if the eigenvalues of $A$ have non-positive real part. We also show that stabilizability does not hold for arbitrary matrices $A$. Moreover, the question of whether the system can be stabilized or not with an arbitrarily large rate of convergence gives rise to a bifurcation phenomenon in dependence of the parameter $μ/T$. | |
| dc.identifier | https://arxiv.org/abs/0810.2122 | |
| dc.identifier | http://arxiv.org/abs/0810.2122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230453 | |
| dc.subject | Optimization and Control | |
| dc.title | On the stabilization of persistently excited linear systems | |
| dc.type | text |