Master-Slave Synchronization for Chaotic Lur’e Systems with Time-Varying Delay Feedback Control via a Quadratic Function Negative-Determination Lemma

This paper mainly examines the problems related to master-slave synchronization control of chaotic Lur’e systems (MSSCLS) which have feedback control with time-varying delay. Above all, the characteristic about nonlinear function vector is fully utilized when the enhanced Lyapunov-Krasovskii functional (LKF) is structured, which takes more time-varying delay crossing terms into account in order to achieve less conservative. Secondly, based on the application of the relaxation integral inequality, the synchronization criterion is improved and derived by the addition of negative-determination lemma of the quadratic function. The improved LKF and the decision lemma under quadratic functions reduce the conservatism of MSSCLS criteria of asymptotic stability. Then, the gain feedback controller and the allowable maximum delay of the feedback control signal are obtained by using the argument setting method under the obtained criterion. Finally, taking Chua’s circuit for instance, the synchronization cruterion’s effectiveness and advantanges are verified by the verdict during the performance comparison of the available approaches in recent years.