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Communication Dans Un Congrès Année : 2009

On the stabilization of permanently excited linear systems

Résumé

We consider control systems of the type x¿ = Ax+¿(t)ub, where u ¿ R, (A; b) is a controllable pair and ¿ is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ¿t+T t ¿ ¿ ¿for 0 < ¿ ¿ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ¿) if the real part of the eigenvalues of A is non positive. The stabilizability does not hold in general for matrices A whose eigenvalues have positive real part. Moreover, the question of whether the system can be stabilized with an arbitrarily large rate of convergence gives rise to a bifurcation phenomenon in dependence of the parameter ¿/T.

Dates et versions

hal-00589702 , version 1 (30-04-2011)

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Yacine Chitour, Mario Sigalotti. On the stabilization of permanently excited linear systems. 48th IEEE Conference on Decision and Control, 2009, Shanghai, China. pp.1100-1105, ⟨10.1109/cdc.2009.5400507⟩. ⟨hal-00589702⟩
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