Asymptotic stabilization for feedforward systems with delayed feedbacks

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. Although exact model knowledge and periodicity of the dynamics are required, 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.