H∞ Control for Master-slave Synchronization of Lur’e Systems with Time-delay Feedback Control

This paper deals with the problems of stability analysis and control synthesis with H∞ performance for the master-slave synchronization of Lur’e systems using a time-delay feedback control. The proposed approach consists in obtaining a new improvedH∞ robust stability criteria as well as a control law based on linear matrix inequalities (LMIs) via discretized Lyapunov–Krasovskii functional combined with an alternative strategy based on the introduction of slack variables to allow the decoupling of the system matrices from the Lyapunov matrices. Using the problem of synchronizing coupled Chua’s circuits, two examples are presented to illustrate the effectiveness of the proposed methodology.