@booklet {CHCHLOSIcdc07, title = {Towards uniform linear time-invariant stabilization of systems with persistency of excitation}, howpublished = {Submitted to CDC 2007}, year = {2007}, month = {December}, address = {New Orleans, USA}, abstract = {

Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizableand $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting. In particular, when $\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback, only depending on $(A,B)$ and the parameters of the persistent excitation, which globally exponentially stabilizes the system? We give a positive answer to this question for two cases: when $A$ is neutrally stable and when the system is the double integrator.

}, keywords = {Robotics}, author = {A. Chaillet and Y. Chitour and A. Lor and M. Sigalotti} }