Weak exponential stability via averaging and applications

Abstract

The averaging method is one of the most powerful methods used to analyze differential equations appearing in the study of nonlinear problems. The averaging method has also been successfully applied in control problems, simplifying the equations and study of the systems involved. In this work, applying the averaging method, we study exponential stability of time varying linear control systems. The obtained results are applied to prove the existence of almost closed relative trajectories for formation flying with single-input control.