Section: New Results

Nonlinear systems with delay

Participants : Frédéric Mazenc [correspondent] , Michael Malisoff [Louisiana State University] , Thach Ngoc Dinh.

We obtained new results on the robustness analysis of nonlinear systems belonging to a general family when they are globally stabilized by a state feedback corrupted by the presence of a delay and sampling [22] , [58] . The result is based on the construction of a non-quadratic Lyapunov-Krasovskii functional.

In [23] , a problem of state feedback stabilization of time-varying feedforward systems with a pointwise delay in the input is solved. The approach we adopted 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 was illustrated through a tracking problem for a model for high level formation flight of unmanned air vehicles.