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.
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).