An Improved Synchronization Criterion for Time-Delayed Lur'e Systems via Cubic Function Negative-Determination Lemma

In this paper, the master-slave synchronization issue of chaotic Lur’ e systems with time-varying-delay feedback control is investigated. Firstly, the synchronization problem of chaotic system is transformed into the stability problem of chaotic synchronization error system, which is studied based on Lyapunov-Krasovskii functional (LKF) method. Secondly, a novel augmented LKF with more cross terms that related to time-varying delay is proposed. Based on the application of the relaxation integral inequality and the reciprocally convex matrix inequality, an improved synchronization criterion is derived by using the cubic function negative-determination lemma. Finally, a numerical simulation example demonstrates the effectiveness and advantages of the proposed methods.