A control perspective on synchronization and the Takens-Aeyels-Sauer Reconstruction Theorem

A method, based on ideas from control theory, is described for the synchronization of discrete time transmitter /receiver dynamics. Conceptually, the methodology consists of constructing observer-receiver dynamics that exploit at each time instant the drive signal and past values of the drive signal. In this way, the method can be viewed as a dynamic reconstruction mechanism. PACS numbers: 02.10.Jf 02.90.+p 05.45.+b 47.52.+j 89.90.+n 1 Introduction Following Pecora and Caroll [14] a huge interest in the synchronization of two coupled systems has arisen. This research is partly motivated by its possible use in secure communications, cf. [6]. Often, like in [14] a drive/response, or transmitter/receiver, viewpoint is assumed. In a discrete-time context, this typically allows for a description of the transmitter as a n-dimensional dynamical system x 1 (k+1) = f 1 (x 1 (k); x 2 (k)) (1) x 2 (k+1) = f 2 (x 1 (k); x 2 (k)) (2) where x 1 (\Delta) and x 2 (\Delta) are vectors of dimension m ..