On the PE stabilization of time-varying systems: open questions and preliminary answers

Abstract : We address the following question: given a double integrator and a linear control that stabilizes it exponentially, is it possible to use the 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; 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 a simple, yet challenging case-study. Our solutions are stated in terms of persistency of excitation.
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Contributor : Gildas Besancon <>
Submitted on : Wednesday, February 25, 2009 - 10:44:37 AM
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Antonio Loria, Antoine Chaillet, Gildas Besancon, Yacine Chitour. On the PE stabilization of time-varying systems: open questions and preliminary answers. Joint 44th IEEE Conference on Decision and Control, and European Control Conference, Dec 2005, Seville, Spain. ⟨hal-00364064⟩

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