Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2008

Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases

Résumé

Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\mu,T$ such that, for every $t\geq 0$, $\int_t^{t+T}\alpha(s)ds\geq \mu$. In particular, when $\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\mu,T$, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when $A$ is neutrally stable and when the system is the double integrator.
Fichier principal
Vignette du fichier
CCLS.pdf (236.62 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00132968 , version 1 (23-02-2007)

Identifiants

Citer

Antoine Chaillet, Yacine Chitour, Antonio Loria, Mario Sigalotti. Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases. Mathematics of Control, Signals, and Systems, 2008, 20 (2), pp.135-156. ⟨10.1007/s00498-008-0024-1⟩. ⟨hal-00132968⟩
230 Consultations
112 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More