Synchronization and Observers for Nonlinear Discrete Time Systems

A method is described for the synchronization of nonlinear discrete time dynamics. The methodology consists of constructing observer-receiver dynamics that exploit at each time instant the drive signal and buffered past values of the drive signal. In this way, the method can be viewed as a dynamic reconstruction mechanism, in contrast to existing static inversion methods from the theory of dynamical systems. Keywords: Synchronization, observers, nonlinear discrete time systems 1 Introduction Following Pecora and Carroll [15] 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 [15] 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) This paper has..

Controlled invariance of nonlinear systems:generalized concepts

A generalized setting is developed, which describes controlled invariance for nonlinear control systems and which incorporates the previous approaches in dealing with controlled invariant distributions. This generalized notion of controlled invariance is of major importance for the geometric description of dynamic feedback problems