Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control

Abstract

This article investigates the robust synchronisation problem for uncertain nonlinear chaotic systems. The norm-bounded uncertainties enter into the chaotic systems in random ways, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequences. For this synchronisation problem, the sampled-data controller that has randomly varying sampling intervals is considered. In order to fully use the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. By the Lyapunov stability theory and the linear matrix inequality (LMI) framework, the existence condition for the sample-date controller that guarantees the robust mean-square synchronisation of chaotic systems is derived in terms of LMIs. Finally, in order to show the effectiveness of our result, the proposed method is applied to two numerical examples: one is Chua's chaotic systems and the other is the hyperchaotic Rössler system.

Keywords:

• nonlinear chaotic systems
• synchronisation
• randomly occurring uncertainties
• variable sampling
• sampled-data control

Acknowledgements

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009373).