Robust Adaptive H∞ Synchronization of Master-Slave Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations

This paper establishes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays, where the mixed delays comprise different discrete and distributed time-delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaption law which include the master-slave parameters are established for designing a delayed synchronization law in terms of linear matrix inequalities. The controller guarantees the H∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example is given to show the effectiveness of the method.