Adaptive synchronization-based approach for real-time identification of coupling delays or node delays in dynamical complex networks

The control and synchronization of time-delayed complex networks have gained considerable attention recently. However, in the existing literature there is few result on the delay estimation in complex networks. In this paper, based on the observer concept and the adaptive synchronization strategy, we present a general and systematic method to estimate the unknown time delays in complex networks. Two kinds of delays, the coupling delays and the node delays, are considered. Several criteria are obtained for the real time identification of the unknown network delays. The local stability of the augmented error systems is proved via the Lyapunov-Krasovskii functional approach and the Barbalat´s Lemma. Two typical examples are presented to verify the effectiveness of the proposed approach.