01263nas a2200157 4500008004100000245009800041210006900139260003100208520065500239653001300894100001600907700001500923700001100938700001700949856013900966 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
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.html