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
Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
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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Article dans une revue
Mathematics of Control, Signals, and Systems, Springer Verlag, 2014, 26 (4), pp.589-616. 〈10.1007/s00498-014-0131-0〉
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Contributeur : Mario Sigalotti <>
Soumis le : lundi 7 octobre 2013 - 17:39:09
Dernière modification le : jeudi 10 mai 2018 - 02:05:57
Document(s) archivé(s) le : vendredi 7 avril 2017 - 08:16:42

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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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