TitleUniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases
Publication TypeMiscellaneous
Year of Publication2007
AuthorsChaillet, A, Chitour, Y, Lor, A, Sigalotti, M

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.