Skip to Main content Skip to Navigation
Journal articles

Growth rates for persistently excited linear systems

Yacine Chitour 1 Fritz Colonius 2 Mario Sigalotti 3, 4
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
4 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider a family of linear control systems $\dot{x}=Ax+\alpha Bu$ where $\alpha$ belongs to a given class of persistently exciting signals. We seek maximal $\alpha$-uniform stabilisation and destabilisation by means of linear feedbacks $u=Kx$. We extend previous results obtained for bidimensional single-input linear control systems to the general case as follows: if the pair $(A,B)$ verifies a certain Lie bracket generating condition, then the maximal rate of convergence of $(A,B)$ is equal to the maximal rate of divergence of $(-A,-B)$. We also provide more precise results in the general single-input case, where the above result is obtained under the sole assumption of controllability of the pair $(A,B)$.
Complete list of metadatas
Contributor : Mario Sigalotti <>
Submitted on : Monday, October 7, 2013 - 5:39:09 PM
Last modification on : Thursday, March 5, 2020 - 6:27:16 PM
Document(s) archivé(s) le : Friday, April 7, 2017 - 8:16:42 AM


Files produced by the author(s)



Yacine Chitour, Fritz Colonius, Mario Sigalotti. Growth rates for persistently excited linear systems. Mathematics of Control, Signals, and Systems, Springer Verlag, 2014, 26 (4), pp.589-616. ⟨10.1007/s00498-014-0131-0⟩. ⟨hal-00851671v2⟩



Record views


Files downloads