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.

10aRobotics1 aChaillet, A1 aChitour, Y1 aLor, A1 aSigalotti, M uhttp://www.centropiaggio.unipi.it/publications/towards-uniform-linear-time-invariant-stabilization-systems-persistency-excitation.html01254nas a2200145 4500008004100000245013000041210006900171520065700240653001300897100001600910700001500926700001100941700001700952856013900969 2007 eng d00aUniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases0 aUniform stabilization for linear systems with persistency of exc3 aConsider 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.

10aRobotics1 aChaillet, A1 aChitour, Y1 aLor, A1 aSigalotti, M uhttp://www.centropiaggio.unipi.it/publications/uniform-stabilization-linear-systems-persistency-excitation-neutrally-stable-and-double