Fault-Tolerant Master–Slave Synchronization for Lur´e Systems Using Time-Delay Feedback Control

This paper deals with fault-tolerant master-slave synchronization for Lur´e systems using time-delay feedback control. Taking a general nature of fault in the master system into account, a new synchronization scheme, namely, fault-tolerant master-slave synchronization, is proposed, by which the master-slave synchronization can be achieved no matter if the fault occurs or not. By making use of an observer-based fault estimator and a modified time-delay feedback controller, the fault-tolerant master-slave synchronization is formulated so as to discuss the global asymptotic stability of the error system and the bound of energy gain from fault to state and fault estimation error vectors. Some new delay-dependent criteria are derived to analyze the synchronization error system, and based on the analysis results, a sufficient condition on the existence of such a master-slave synchronization scheme and a solution to the controller and fault-estimator gain matrices are obtained in terms of linear matrix inequalities. Finally, a Chua´s circuit is used to illustrate the effectiveness of the proposed method.