Growth rates for persistently excited linear systems

Yacine Chitour; Fritz Colonius; Mario Sigalotti

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arXiv · 1308.3758

Growth rates for persistently excited linear systems

Yacine Chitour·Fritz Colonius·Mario Sigalotti

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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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Yacine Chitour, Fritz Colonius, Mario Sigalotti. 2013-08-17. Growth rates for persistently excited linear systems. https://arxiv.org/abs/1308.3758

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