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Abstract

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 ...
... From a control perspective, the problem of synchronization can be regarded as an observer problem, cf. [13] for continuous-time and [5] for discrete-time systems. This work focuses on a design of nonlinear observers for discrete-time systems (transmitters) of the form ...
... For w = ǫ, system (5.24) is identical to the one presented in [1]. An observer design via EOF for w = ǫ was already considered in [5]. ...
... 3) The n-time delayed value of u, u n− is restituted in the last reconstructed dynamic. This approach could seem not at all original because in [5], [6], [10] the idea of a " delayed observer " was developed. The authors, used the (i − N )-times delayed values of the output y in order to observe the i-th dynamic. ...
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