# Growth rates for persistently excited linear systems

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 $(A,B)$.
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https://hal.inria.fr/hal-00851671
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

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CCS-3-10-2013.pdf
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### Citation

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⟩

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