Separation and synchronization of piecewise linear chaotic systems

In this paper a topic regarding the synchronization of chaotic systems is dealt with: the case of separation and synchronization of many chaotic signals generated by different chaotic circuits and combined together is examined. In particular, an observer based strategy has been adopted, and an approach for the simultaneous stabilization of many Luenberger observers has been investigated to face the problem of separation and synchronization. The design strategy is based on linear matrix inequalities (LMIs). Indeed, the LMI problem is referred to have a solution if a dual optimization problem admits a solution. In our case the feasibility condition, if it does exist, allows us to establish that the separation and synchronization problem for the chosen circuit admits a solution. Some numerical simulations are reported. Further results refer to an experimental circuit showing the suitability of the approach. Furthermore, the use of the proposed scheme to transmit two or more information masked into two or more multiplexed chaotic signals and the design of suitable parameters through the introduced technique based on LMIs are discussed.