Observer-Based Exponential Synchronization of Chaotic Multimodels
Résumé
This paper deals with the design of observers for a class of nonlinear systems. Nonlinear multimodels represent a way to generate new families of chaotic systems, from p chaotic basis models. These multimodels can be used for synchronization purpose, since the signal transmitted to the receiver is a real mixing -and not switching- of p chaotic basis models and may thwart delay reconstruction based attacks. This kind of attacks takes advantage of the information contained in long time series of a unique attractor, which is not the case here. We provide specific observers for this class of nonlinear systems, preventing from any loss of synchronization, contrary to one can expect. Exponential synchronization is proved under sufficient conditions, expressed in terms of Bilinear and Linear Matrix Inequalities. Our results are illustrated on the example of two basis Chua's circuits. In addition to the implementation of exponential state estimation of the resulting multimodel, some numerical evidence of its chaotic behavior is shown through a bifurcation diagram. The proposed synchronization scheme is then included into a communication system. The security level is analyzed with respect to Kerckhoff principle: the security relies only on the secret key. The end of the paper is devoted to a study of the sensibility of the key to slight mismatches between the transmitter and the receiver, and we showed that the multimodel based cryptosystem possesses the confusion and diffusion properties, which prevents it from common cryptanalysis.