# H(infini)-feedback design for linear systems subject to input saturation

Abstract : In this paper, we study gain attenuation of linear systems subject to input saturation $\dot x=Ax+b\sg(u)$. In case there exists a family $\cal{K}$ of stabilizing feedback, we address the issue of estimating the infimum of $\gamma_k$, the gain of the output map $v\mapsto x_v$, defined for $k\in {\cal{K}}$, and where $x_v$ is the solution of $\dot x=Ax+b\sg(k(x)+v)$ starting at zero. For the 2D oscillator and double integrator, we explicitely determine an appropriate family $\cal{K}$ of stabilizing feedback and prove that the infimum over the gains is equal to zero.
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https://hal.archives-ouvertes.fr/hal-00578908
Contributor : Myriam Baverel <>
Submitted on : Wednesday, March 23, 2011 - 9:36:16 AM
Last modification on : Thursday, April 5, 2018 - 12:30:05 PM
Long-term archiving on : Thursday, November 8, 2012 - 12:21:03 PM

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• HAL Id : hal-00578908, version 1

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Yacine Chitour, Sami Tliba. H(infini)-feedback design for linear systems subject to input saturation. 2011. ⟨hal-00578908⟩

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