01253nas a2200157   4500008004100000245009800041210006900139260003100208520065500239653001300894100001600907700001500923700001100938700001700949856012900966       2007                        eng d00aTowards uniform linear time-invariant stabilization of systems with persistency of excitation0 aTowards uniform linear timeinvariant stabilization of systems wi  aNew Orleans, USAcDecember3 a<p>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.</p>
10aRobotics1 aChaillet, A1 aChitour, Y1 aLor, A1 aSigalotti, M  uhttp://615830.rige.asia/publications/towards-uniform-linear-time-invariant-stabilization-systems-persistency-excitation.html01244nas a2200145   4500008004100000245013000041210006900171520065700240653001300897100001600910700001500926700001100941700001700952856012900969       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 a<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>
10aRobotics1 aChaillet, A1 aChitour, Y1 aLor, A1 aSigalotti, M  uhttp://615830.rige.asia/publications/uniform-stabilization-linear-systems-persistency-excitation-neutrally-stable-and-double