Adaptive H<SUB align="right">&infin; synchronisation of two different general chaotic systems with external disturbances

Abstract

We investigate the synchronisation of two different general chaotic systems with external disturbances via the adaptive H ∞ control technique. Based on the Lyapunov stability theory and linear matrix inequality (LMI), several adaptive H ∞ synchronisation schemes are established which guarantee robust asymptotically synchronisation for the drive system and the noise-perturbed response system as well as achieving a prescribed robust H ∞ performance level. Finally, the Lorenz system and the noise-perturbed Rössler system are taken as an example to analyse the adaptive H ∞ synchronisation process. The numerical simulations have shown the correctness and effectiveness of the proposed methods.