Averaging Theory for Delay Difference Equations with Time-Varying Delays

Although the theory of averaging has long been a classical component of applied mathematics, it has found new importance in controls engineering because of the development of adaptive identification, adaptive control, and open-loop oscillatory control. In this paper, we develop a theory of averaging on both finite and infinite time intervals for delay difference equations with time-varying delays. The main results of this paper are applied to the adaptive identification of a pipe mixing problem in the presence of time-varying transport delays.