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

摘要

In this paper, we study gain attenuation of linear systems subject to input saturation $dot x=Ax+bsg(u)$. 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 $vmapsto x_v$, defined for $kin {cal{K}}$, and where $x_v$ is the solution of $dot x=Ax+bsg(k(x)+v)$ 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.