High gain observer with algorithm transformation to extended Jordan observable form for chaos synchronization applications

This work is concerned with the high gain observer design for a class of a third order ordinary differential equation chaotic nonlinear system for chaos communications applications. For this, we consider mainly the Rossler model as drive oscillator. We start by transforming the Rossler equations into the so-called Extended Jordan Controllable Form in order to facilitate the construction of the observer´s gain. It is shown that synchronization is achieved under a typical unidirectional master-slave configuration by using the receiver as the observer. The designed observer is tested against initial conditions mismatch, delay and noise presence via Matlab Simulink simulation in sight of potential application to real communication systems. The proposed observer shows good quality convergence performance. A chaotic masking scheme making use of the transformed Rossler observer is implemented in order to provide a descriptive example of a chaos communication system with the presented methodology.