@booklet {CHCHLOSI07,
	title = {Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases},
	howpublished = {Submitted to Mathematics of Control, Signals and Systems},
	year = {2007},
	abstract = {<p>Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ 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 asymptotically 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.</p>
},
	keywords = {Robotics},
	author = {A. Chaillet and Y. Chitour and A. Lor and M. Sigalotti}
}
