Title Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases Publication Type Miscellaneous Year of Publication 2007 Authors Chaillet, A, Chitour, Y, Lor, A, Sigalotti, M Keywords Robotics Abstract 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.