Generalized lag-synchronization of chaotic mix-delayed systems with uncertain parameters and unknown perturbations

Chaotic systems in practice are always influenced by some unknown factors, which may make the chaotic behavior completely different from that of unaffected system. In this paper, generalized lag-synchronization for a general class of coupled chaotic systems with mixed delays, uncertain parameters, as well as external perturbations is investigated. A simple but all-powerful robust adaptive controller is designed to achieve this goal. Based on Lyapunov stability theory, integral inequality and Barbalat lemma, rigorous proofs are given for the asymptotic stability of the error systems of the coupled systems with or without external perturbations. Sufficient conditions for inaccuracy or accuracy estimation of unknown parameters are also given. Moreover, the designed adaptive controller has better anti-interference capacity than those of references. Numerical simulations verify the effectiveness of the theoretical results.