TitleOn the PE stabilization of time-varying systems: open questions and preliminary answers
Publication TypeConference Paper
Year of Publication2005
Conference NameProc. IEEE Int. Conf. on Decision and Control
Date PublishedDecember
Publication Languageeng
AuthorsLor, A, Chaillet, A, Besancon, G, Chitour, Y
Conference LocationSevilla, Spain

We address the following fundamental question: given a double integrator and a linear control that stabilizes it exponentially, is it possible to use the {\em same} control input in the case that the control input is multiplied by a time-varying term? Such question has many interesting motivations and generalizations: 1) we can pose the same problem for an input gain that depends on the state and time hence, a specific persistency of excitation property for nonlinear systems must be imposed; 2) the stabilization –with the same method– of chains of integrators of higher order than two is fundamentally more complex and has applications in the stabilization of driftless systems; 3) the popular backstepping method stabilization method for systems with non-invertible input terms. The purpose of this note is two-fold: we present some open questions that we believe are significant in time-varying stabilization and present some preliminary answers for simple, yet challenging case-studies.