Asymptotic Stabilization for Feedforward Systems with Delayed Feedback

Abstract : A problem of state feedback stabilization of time-varying feedforward systems with a pointwise delay in the input is solved. The approach relies on a time-varying change of coordinates and Lyapunov-Krasovskii functionals. The result applies for any given constant delay, and provides uniformly globally asymptotically stabilizing controllers of arbitrarily small amplitude. The closed-loop systems enjoy input-to-state stability properties with respect to additive uncertainty on the controllers. The work is illustrated through a tracking problem for a model for high level formation flight of unmanned air vehicles.